Bohmian trajectories for photons

Bohmian particle trajectories contradict quantum mechanics

The Bohmian interpretation of quantum mechanics adds particle trajectories to the wave function and ensures that the probability distribution of the particle positions agrees with quantum mechanics at any time. This is not sufficient to avoid contradictions with quantum mechanics. There are correlations between particle positions at different times which cannot be reproduced with real particle trajectories. A simple rearrangement of an experimental test of the Bell-CHSH inequality demonstrates this.

Local-realistic Bohmian trajectories: a non-Bohmian approach to wave-particle duality

We present a local-realistic description of both wave-particle duality and Bohmian trajectories. Our approach is relativistic and based on Hamilton's principle of classical mechanics, but departs from its standard setting in two respects. First, we address an ensemble of extremal curves, the so-called Mayer field, instead of focusing on a single extremal curve. Second, we assume that there is a scale, below which we can only probabilistically assess which extremal curve in the ensemble is actually realized. The continuity equation ruling the conservation of probability represents a subsidiary …

Bohmian trajectories for bipartite entangled states

We derive Bohm's trajectories from Bell's beables for arbitrary bipartite systems composed by dissipative noninteracting harmonic oscillators at finite temperature. As an application of our result, we calculate the Bohmian trajectories of particles described by a generalized Werner state, comparing the trajectories when the sate is either separable or entangled. We show that qualitative differences appear in the trajectories for entangled states as compared with those for separable states.

Origin of chaos in 3-d Bohmian trajectories

We study the 3-d Bohmian trajectories of a quantum system of three harmonic oscillators. We focus on the mechanism responsible for the generation of chaotic trajectories. We demonstrate the existence of a 3-d analogue of the mechanism found in earlier studies of 2-d systems, based on moving 2-d `nodal point - X-point complexes'. In the 3-d case, we observe a foliation of nodal point - X-point complexes, forming a `3-d structure of nodal and X-points'. Chaos is generated when the Bohmian trajectories are scattered at one or more close encounters with such a structure.

Bohmian trajectories and the ether: Where does the analogy fail?

Once considered essential to the explanation of electromagnetic phenomena, the ether was eventually discarded after the advent of special relativity. The lack of empirical signature of realist interpretative schemes of quantum mechanics, like Bohmian trajectories, has led some to conclude that, just like the ether, they can be dispensed with, replaced by the corresponding emergence of the concept of information. Although devices like Bohmian trajectories and the ether do present important analogies, I argue that there is also a crucial difference, related to distinct explanatory functions of q…

Wave Functions and Bohmian Trajectories in Interference Phenomena

In the last few years the hydrodynamic formulation of quantum mechanics, equivalent to the Bohmian equations of motion, has been used to obtain numerical solutions of the Schrodinger equation. Problems, however, have been experienced near wave function nodes (or low probability regions). Here we attempt to compute wave functions and Bohmian trajectories for the interference of one particle or of two identical particles. It turns out that the large number of nodes (i.e. interference minima) makes the hydrodynamic equations impractical, whereas a more straightforward solution of the Schrodinger …

Partial Integrability of 3-d Bohmian Trajectories

In this paper we study the integrability of 3-d Bohmian trajectories of a system of quantum harmonic oscillators. We show that the initial choice of quantum numbers is responsible for the existence (or not) of an integral of motion which confines the trajectories on certain invariant surfaces. We give a few examples of orbits in cases where there is or there is not an integral and make some comments on the impact of partial integrability in Bohmian Mechanics. Finally, we make a connection between our present results for the integrability in the 3-d case and analogous results found in the 2-d a…

Bohmian trajectories for the half-line barrier

Bohmian trajectories are considered for a particle that is free (i.e. the potential energy is zero), except for a half-line barrier. On the barrier, both Dirichlet and Neumann boundary conditions are considered. The half-line barrier yields one of the simplest cases of diffraction. Using the exact time-dependent propagator found by Schulman, the trajectories are computed numerically for different initial Gaussian wave packets. In particular, it is found that different boundary conditions may lead to qualitatively different sets of trajectories. In the Dirichlet case, the particles tend to be m…

Scattering by a reflectionless modified Pöschl-Teller potential: Bohmian trajectories and arrival times

A nonreflecting wavepacket is constructed by the superposition of reflectionless eigenstates of sech2 potential. Free propagation and propagation in the presence of the above potential of such a wavepacket is considered using the concept of arrival time. Comparison is made with the free evolving Gaussian wavepacket. Mean arrival time at a detector behind the well is given as a function of mass for separate cases. A selection of Bohmian trajectories in the interacting case are computed and compared to the trajectories of a free particle guided by a Gaussian packet.

量子可观测量的动力学与玻姆量子力学中的玻恩规则

Dynamics of quantum observables and Born's rule in Bohmian Quantum Mechanics

本文研究了各向异性二维量子谐振子中玻姆轨迹的有序与混沌特性，通过标准量子力学和玻姆力学计算能量、动量等可观测量平均值，并分析不同节点波函数下轨迹类型对平均值的贡献。

Surrealistic Bohmian trajectories do not occur with macroscopic pointers

We discuss whether position measurements in quantum mechanics can be contradictory with Bohmian trajectories, leading to what has been called \textquotedblleft surrealistic trajectories\textquotedblright\ in the literature. Previous work has considered that a single Bohmian position can be ascribed to the pointer. Nevertheless, a correct treatment of a macroscopic pointer requires that many particle positions should be included in the dynamics of the system, and that statistical averages should be made over their random initial values. Using numerical as well as analytical calculations, we sho…

Asymptotic velocities in quantum and Bohmian mechanics

In this paper the relations between the asymptotic velocity operators of a quantum system and the asymptotic velocities of the associated Bohmian trajectories are studied. In particular it is proved that, under suitable conditions of asymptotic regularity, the probability distribution of the asymptotic velocities of the Bohmian trajectories is equal to the one derived from the asymptotic velocity operators of the associated quantum system. It is also shown that in the relativistic case the distribution of the asymptotic velocities of the Bohmian trajectories is covariant, or equivalently, it d…

Global existence and uniqueness of Bohmian trajectories

It is shown that Bohmian mechanics is internally consistent in the sense that the equations of motion typically have global solutions despite the fact that the velocity field is singular at the nodes of the wave function and at other points. This result is fundamental for the derivation of the quantum formalism. The role of the quantum flux is emphasized.

观测单光子的相对论轨迹

Observing relativistic trajectories of single photons

本研究在迈克尔逊-萨格纳克干涉仪中实验重构了单光子的相对论玻姆轨迹，观测到其轨迹的亚光速与超光速特征，为探索相对论玻姆力学的特殊特性提供了实验途径。

Bohmian Trajectories as the Foundation of Quantum Mechanics

Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schroedinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding that is as clear as that of classical mechanics. Indeed, they succeed in serving that purpose in the context of a theory known as Bohmian mechanics, to which this article is an introduction.

Bohmian Mechanics

Bohmian mechanics is a theory about point particles moving along trajectories. It has the property that in a world governed by Bohmian mechanics, observers see the same statistics for experimental results as predicted by quantum mechanics. Bohmian mechanics thus provides an explanation of quantum mechanics. Moreover, the Bohmian trajectories are defined in a non-conspiratorial way by a few simple laws.

Generic Bohmian Trajectories of an Isolated Particle

The generic Bohmian trajectories are calculated for an isolated particle in an approximate energy eigenstate, for an arbitrary one-dimensional potential well. It is shown, that the necessary and sufficient condition for there to be a negligible probability of the trajectory deviating significantly from the classical trajectory at any stage in the motion is, that the state be a narrowly localised wave packet. The properties of the Bohmian trajectories are discussed in relationship to the theory of retrodictively optimal simultaneous measurements of position and momentum which was presented in s…

Weak measurements of trajectories in quantum systems: classical, Bohmian and sum over paths

Weak values, obtained from weak measurements, attempt to describe the properties of a quantum system as it evolves from an initial to a final state, without practically altering this evolution. Trajectories can be defined from weak measurements of the position, or inferred from weak values of the momentum operator. The former can be connected to the asymptotic form of the Feynman propagator and the latter to Bohmian trajectories. Employing a time-dependent oscillator as a model, this work analyzes to what extent weak measurements can shed light on the underlying dynamics of a quantum system ex…

Chaos in Bohmian Quantum Mechanics: A short review

This is a short review in the theory of chaos in Bohmian Quantum Mechanics based on our series of works in this field. Our first result is the development of a generic theoretical mechanism responsible for the generation of chaos in an arbitrary Bohmian system (in 2 and 3 dimensions). This mechanism allows us to explore the effect of chaos on Bohmian trajectories and study in detail (both analytically and numerically) the different kinds of Bohmian trajectories where, in general, chaos and order coexist. Finally we explore the effect of quantum entanglement on the evolution of the Bohmian traj…

Bohmian trajectories and quantum phase space distributions

We prove that most quasi-distributions can be written in a form similar to that of the de Broglie-Bohm distribution, except that ordinary products are replaced by some suitable non-commutative star product. In doing so, we show that the Hamilton-Jacobi trajectories and the concept of "classical pure state" are common features to all phase space formulations of quantum mechanics. Furthermore, these results provide an explicit quantization prescription for classical distributions.

N-Slit Interference: Fractals in Near-Field Region, Bohmian Trajectories

Scattering cold particles on an $N$-slit grating is shown to reproduce an interference pattern, that manifests itself in the near-field region as the fractal Talbot carpet. In the far-field region the pattern is transformed to an ordinary diffraction, where principal beams are partitioned from each other by ($N-2$) weak ones. A probability density plot of the wave function, to be represented by a gaussian wavepacket, is calculated both in the near-field region and in the far-field one. Bohmian (geodesic) trajectories, to be calculated by a guidance equation, are superimposed on the probability…

Monte Carlo Generation of Bohmian Trajectories

We report on a Monte Carlo method that generates one-dimensional trajectories for Bohm's formulation of quantum mechanics that doesn't involve differentiation or integration of any equations of motion. At each time, t=nδt (n=1,2,3,...), N particle positions are randomly sampled from the quantum probability density. Trajectories are built from the sorted N sampled positions at each time. These trajectories become the exact Bohm solutions in the limits N->\infty and δt -> 0. Higher dimensional problems can be solved by this method for separable wave functions. Several examples are given, includi…

Bohmian trajectories and the Path Integral Paradigm. Complexified Lagrangian Mechanics

David Bohm shown that the Schr{ö}dinger equation, that is a "visiting card" of quantum mechanics, can be decomposed onto two equations for real functions - action and probability density. The first equation is the Hamilton-Jacobi (HJ) equation, a "visiting card" of classical mechanics, to be modified by the Bohmian quantum potential. And the second is the continuity equation. The latter can be transformed to the entropy balance equation. The Bohmian quantum potential is transformed to two Bohmian quantum correctors. The first corrector modifies kinetic energy term of the HJ equation, and the s…

Bohmian Trajectories of Airy Packets

The discovery of Berry and Balazs in 1979 that the free-particle Schrödinger equation allows a non-dispersive and accelerating Airy-packet solution has taken the folklore of quantum mechanics by surprise. Over the years, this intriguing class of wave packets has sparked enormous theoretical and experimental activities in related areas of optics and atom physics. Within the Bohmian mechanics framework, we present new features of Airy wave packet solutions to Schrödinger equation with time-dependent quadratic potentials. In particular, we provide some insights to the problem by calculating the c…

Flux Continuity and Probability Conservation in Complexified Bohmian Mechanics

Recent years have seen increased interest in complexified Bohmian mechanical trajectory calculations for quantum systems, both as a pedagogical and computational tool. In the latter context, it is essential that trajectories satisfy probability conservation, to ensure they are always guided to where they are most needed. In this paper, probability conservation for complexified Bohmian trajectories is considered. The analysis relies on time-reversal symmetry considerations, leading to a generalized expression for the conjugation of wavefunctions of complexified variables. This in turn enables m…

用玻姆轨迹理解量子电动力学：检测非本体光子

A simple understanding of quantum electrodynamics using Bohmian trajectories: detecting non-ontic photons

本文通过玻姆轨迹方法研究量子光学，展示如何用电子轨迹和电磁场模拟光子现象，阐明非本体光子的测量意义。

Proposal to demonstrate the non-locality of Bohmian mechanics with entangled photons

Bohmian mechanics reproduces all statistical predictions of quantum mechanics, which ensures that entanglement cannot be used for superluminal signaling. However, individual Bohmian particles can experience superluminal influences. We propose to illustrate this point using a double double-slit setup with path-entangled photons. The Bohmian velocity field for one of the photons can be measured using a recently demonstrated weak-measurement technique. The found velocities strongly depend on the value of a phase shift that is applied to the other photon, potentially at spacelike separation.

Bohmian Trajectories For a Time Foliation with Kinks

This paper concerns the hypersurface Bohm-Dirac model, i.e., the version of Bohmian mechanics in a relativistic space-time proposed by Dürr et al. [1], which assumes a preferred foliation of space-time into spacelike hypersurfaces (called the time foliation) as given. We show that the leaves of the time foliation do not have to be smooth manifolds but can be allowed to have kinks. More precisely, we show that, also for leaves with kinks, the trajectories are still well defined and the appropriate $|ψ|^2$ distribution is still equivariant, so that the theory is still empirically equivalent to s…

Dividing Line between Quantum and Classical Trajectories: Bohmian Time Constant

This work proposes an answer to a challenge posed by Bell on the lack of clarity in regards to the line between the quantum and classical regimes in a measurement problem. To this end, a generalized logarithmic nonlinear Schrödinger equation is proposed to describe the time evolution of a quantum dissipative system under continuous measurement. Within the Bohmian mechanics framework, a solution to this equation reveals a novel result: it displays a time constant which should represent the dividing line between the quantum and classical trajectories. It is shown that continuous measurements and…

On the importance of the Bohmian approach for interpreting CP-violation experiments

We argue that the inference of CP violation in experiments involving the $K^0-\bar{K^0}$ system in weak interactions of particle physics is facilitated by the assumption of particle trajectories for the decaying particles and the decay products. A consistent explanation in terms of such trajectories is naturally incorporated within the Bohmian interpretation of quantum mechanics.

Quantum initial value representations using approximate Bohmian trajectories

Quantum trajectories, originating from the de Broglie-Bohm (dBB) hydrodynamic description of quantum mechanics, are used to construct time-correlation functions in an initial value representation (IVR). The formulation is fully quantum mechanical and the resulting equations for the correlation functions are similar in form to their semi-classical analogs but do not require the computation of the stability or monodromy matrix or conjugate points. We then move to a {\em local} trajectory description by evolving the cumulants of the wave function along each individual path. The resulting equation…

Bohmian trajectories in an entangled two-qubit system

In this paper we examine the evolution of Bohmian trajectories in the presence of quantum entanglement. We study a simple two-qubit system composed of two coherent states and investigate the impact of quantum entanglement on chaotic and ordered trajectories via both numerical and analytical calculations.

Can Bohmian trajectories account for quantum recurrences having classical periodicities?

Quantum systems in specific regimes display recurrences at the period of the periodic orbits of the corresponding classical system. We investigate the excited hydrogen atom in a magnetic field -- a prototypical system of 'quantum chaos' -- from the point of view of the de Broglie Bohm (BB) interpretation of quantum mechanics. The trajectories predicted by BB theory are computed and contrasted with the time evolution of the wavefunction, which shows pronounced features at times matching the period of closed orbits of the classical hydrogen in a magnetic field problem. Individual BB trajectories…

Bohmian mechanics, the quantum-classical correspondence and the classical limit: the case of the square billiard

Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum amplitude being controlled by the spread of the corresponding classical statistical distribution. We investigate wavepacket dynamics and compute the corresponding de Broglie-Bohm trajectories in the quantum square billiard. We also determine the trajectories and statistical distribution dynamics for the equivalent classical billiard. Individual Bohmian trajec…

Why Bohmian Mechanics? one and two-time position measurements, Bell inequalities, philosophy and physics

In Bohmian mechanics particles follow continuous trajectories, hence 2-time position correlations are well defined. Nevertheless, Bohmian mechanics predicts the violation of Bell inequalities. Motivated by this fact we investigate position measurements in Bohmian mechanics by coupling the particles to macroscopic pointers. This explains the violation of Bell inequalities despite 2-time position correlations. We relate this fact to so-called surrealistic trajectories that, in our model, correspond to slowly moving pointers. Next, we emphasize that the nice feature of Bohmian mechanics, which do…

Uniqueness of Bohmian Mechanics, and Solutions From Probability Conservation

We show that one-dimensional Bohmian mechanics is unique, in that, the Bohm trajectories are the only solutions that conserve total left (or right) probability. In Brandt et al., Phys. Lett. A, 249 (1998) 265--270, they define quantile motion--unique trajectories are solved by assuming that the total probability on each side of the particle is conserved. They argue that the quantile trajectories are identical to the Bohm trajectories. Their argument, however, fails to notice the gauge freedom in the definition of the quantum probability current. Our paper sidesteps this under-determinedness of…

Chaotic trajectories in complex Bohmian systems

We consider the Bohmian trajectories in a 2-d quantum harmonic oscillator with non commensurable frequencies whose wavefunction is of the form $Ψ=aΨ_{m_1,n_1}(x,y)+bΨ_{m_2,n_2}(x,y)+cΨ_{m_3,n_3}(x,y)$. We first find the trajectories of the nodal points for different combinations of the quantum numbers $m,n$. Then we study, in detail, a case with relatively large quantum numbers and two equal $m's$. We find %We find first the nodal points where $Ψ=0$. The nodes can be found analytically only if $m$ and $n$ are small. If two $m's$ (or two $n's$ are equal we can find explicitly the nodal points ,…

隧道光子对玻姆力学不构成挑战

Tunneling photons pose no challenge to Bohmian mechanics

本文指出，Sharoglazova等人实验中观测到的半经典速度与玻姆速度差异不构成对玻姆力学的挑战，因两者物理量本质不同，且两种解释在耦合波导中预测的光子隧穿动力学完全一致。

Entangled Quantum Dynamics of Many-Body Systems using Bohmian Trajectories

Bohmian mechanics is an interpretation of quantum mechanics that describes the motion of quantum particles with an ensemble of deterministic trajectories. Several attempts have been made to utilize Bohmian trajectories as a computational tool to simulate quantum systems consisting of many particles, a very demanding computational task. In this paper, we present a novel ab-initio approach to solve the many-body problem for bosonic systems by evolving a system of one-particle wavefunctions representing pilot waves that guide the Bohmian trajectories of the quantum particles. In this approach, qu…

Chaos and ergodicity in entangled non-ideal Bohmian qubits

We study the Bohmian dynamics of a large class of bipartite systems of non-ideal qubit systems, by modifying the basic physical parameters of an ideal two-qubit system, made of coherent states of the quantum harmonic oscillator. First we study the case of coherent states with truncated energy levels and large amplitudes. Then we study non-truncated coherent states but with small amplitudes and finally a combination of the above cases. In all cases we find that the chaotic Bohmian trajectories are approximately ergodic. We also study the number and the spatial arrangement of the nodal points of…

Chaos in 2-d Bohmian Trajectories

We make a short review of the most general mechanism for the generation of chaos in 2-d Bohmian trajectories, the so called `nodal point-X-point complex' (NPXPC) mechanism. The presentation is based on numerical calculations made with Maple and is enriched with new results on the details of the generation of chaos, and the form of the potential around the NPXPC.

Bohmian Classical Limit in Bounded Regions

Bohmian mechanics is a realistic interpretation of quantum theory. It shares the same ontology of classical mechanics: particles following continuous trajectories in space through time. For this ontological continuity, it seems to be a good candidate for recovering the classical limit of quantum theory. Indeed, in a Bohmian framework, the issue of the classical limit reduces to showing how classical trajectories can emerge from Bohmian ones, under specific classicality assumptions. In this paper, we shall focus on a technical problem that arises from the dynamics of a Bohmian system in bounded…

Bohmian Mechanics, Collapse Models and the emergence of Classicality

We discuss the emergence of classical trajectories in Bohmian Mechanics (BM), when a macroscopic object interacts with an external environment. We show that in such a case the conditional wave function of the system follows a dynamics which, under reasonable assumptions, corresponds to that of the Ghirardi-Rimini-Weber (GRW) collapse model. As a consequence, Bohmian trajectories evolve classically. Our analysis also shows how the GRW (istantaneous) collapse process can be derived by an underlying continuous interaction of a quantum system with an external agent, thus throwing a light on how co…

Bohmian trajectories for Kerr-Newman particles in complex space-time

Complexified Lienard-Wiechert potentials simplify the mathematics of Kerr-Newman particles. Here we constrain them by fiat to move along Bohmian trajectories to see if anything interesting occurs, as their equations of motion are not known. A covariant theory due to Stueckelberg is used. This paper deviates from the traditional Bohmian interpretation of quantum mechanics since the electromagnetic interactions of Kerr- Newman particles are dictated by general relativity. A Gaussian wave function is used to produce the Bohmian trajectories, which are found to be multi-valued. A generalized analy…

Relativistic Bohmian trajectories of photons via weak measurements

Bohmian mechanics is a nonlocal hidden-variable interpretation of quantum theory which predicts that particles follow deterministic trajectories in spacetime. Historically, the study of Bohmian trajectories has mainly been restricted to nonrelativistic regimes due to the widely held belief that the theory is incompatible with special relativity. Here we derive expressions for the relativistic velocity and spacetime trajectories of photons in a Michelson-Sagnac-type interferometer. The trajectories satisfy quantum-mechanical continuity and the relativistic velocity addition rule. Our new veloci…

Bohmian Trajectories Post-Decoherence

The proposal that the interaction between a macroscopic body and its environment plays a crucial role in producing the correct classical limit in the Bohm interpretation of quantum mechanics is investigated, in the context of a model of quantum Brownian motion. It is well known that one of the effects of the interaction is to produce an extremely rapid approximate diagonalisation of the reduced density matrix in the position representation. This effect is, by itself, insufficient to produce generically quasi-classical behaviour of the Bohmian trajectory. However, it is shown that, if the syste…

Analysis of strong-field enhanced ionization of molecules using Bohmian trajectories

We theoretically investigate the mechanism of enhanced ionization in two-electron molecules by analyzing Bohmian trajectories for a one-dimensional H2 in an intense laser field. We identify both types of ionizing trajectories corresponding to the ejection from the up-field and down-field cores. The trajectories of the two electrons are correlated with each other in the former while correlation is negligible in the latter. The contributions from the two ionization types, though depending on laser intensity and internuclear distance, are comparable to each other.

Bohmian trajectories and Klein's paradox

We compute the Bohmian trajectories of the incoming scattering plane waves for Klein's potential step in explicit form. For finite norm incoming scattering solutions we derive their asymptotic space-time localization and we compute some Bohmian trajectories numerically. The paradox, which appears in the traditional treatments of the problem based on the outgoing scattering asymptotics, is absent.

Experimental nonlocal steering of Bohmian trajectories

Interpretations of quantum mechanics (QM), or proposals for underlying theories, that attempt to present a definite realist picture, such as Bohmian mechanics, require strong non-local effects. Naively, these effects would violate causality and contradict special relativity. However if the theory agrees with QM the violation cannot be observed directly. Here, we demonstrate experimentally such an effect: we steer the velocity and trajectory of a Bohmian particle using a remote measurement. We use a pair of photons and entangle the spatial transverse position of one with the polarization of the…

Bohmian Trajectories for Hamiltonians with Interior-Boundary Conditions

Recently, there has been progress in developing interior-boundary conditions (IBCs) as a technique of avoiding the problem of ultraviolet divergence in non-relativistic quantum field theories while treating space as a continuum and electrons as point particles. An IBC can be expressed in the particle-position representation of a Fock vector $ψ$ as a condition on the values of $ψ$ on the set of collision configurations, and the corresponding Hamiltonian is defined on a domain of vectors satisfying this condition. We describe here how Bohmian mechanics can be extended to this type of Hamiltonian…

Reconciling Semiclassical and Bohmian Mechanics: I. Stationary states

The semiclassical method is characterized by finite forces and smooth, well-behaved trajectories, but also by multivalued representational functions that are ill-behaved at turning points. In contrast, quantum trajectory methods--based on Bohmian mechanics (quantum hydrodynamics)--are characterized by infinite forces and erratic trajectories near nodes, but also well-behaved, single-valued representational functions. In this paper, we unify these two approaches into a single method that captures the best features of both, and in addition, satisfies the correspondence principle. Stationary eige…

N-slit interference: Path integrals, Bohmian trajectories

Path integrals give a possibility to compute in details routes of particles from particle sources through slit gratings and further to detectors. The path integral for a particle passing through the Gaussian slit results in the Gaussian wavepacket. The wavepackets prepared on N slits and superposed together give rise to interference pattern in the near-field zone. It transforms to diffraction in the far-field zone represented by divergent principal rays, at that all rays are partitioned from each other by (N-2) subsidiary rays. The Bohmian trajectories in the near-field zone of N-slit gratings…

What is Surrealistic about Bohm Trajectories?

We discuss interferometers in Bohmian quantum mechanics. It is shown that, with the correct configuration space, Bohm trajectories in a which way interferometer are not surrealistic, but behaves exactly as common sense suggests. Some remarks about a way to generalize Bohmian mechanics to treat density matrix are also made. PACS: 03.65.Bz, 03.75.Dg Key words: Bohm Trajectories, Which Way Interferometers, ESSW

On the classical limit of Bohmian mechanics for Hagedorn wave packets

We consider the classical limit of quantum mechanics in terms of Bohmian trajectories. For wave packets as defined by Hagedorn we show that the Bohmian trajectories converge to Newtonian trajectories in probability.