Revisiting the Schrodinger probability current

Testing Quantum Coherence in Stochastic Electrodynamics with Squeezed Schrödinger Cat States

The interference pattern in electron double-slit diffraction is a hallmark of quantum mechanics. A long standing question for stochastic electrodynamics (SED) is whether or not it is capable of reproducing such effects, as interference is a manifestation of quantum coherence. In this study, we use excited harmonic oscillators to directly test this quantum feature in SED. We use two counter-propagating dichromatic laser pulses to promote a ground-state harmonic oscillator to a squeezed Schrödinger cat state. Upon recombination of the two well-separated wavepackets, an interference pattern emerg…

Fractional Schrodinger equation

Properties of the fractional Schrodinger equation have been studied. We have proven the hermiticity of fractional Hamilton operator and established the parity conservation law for the fractional quantum mechanics. As physical applications of the fractional Schrodinger equation we have found the energy spectrum for a hydrogen-like atom - fractional ''Bohr atom'' and the energy spectrum of fractional oscillator in the semiclassical approximation. A new equation for the fractional probability current density has been developed and discussed. We also discuss the relationships between the fractiona…

重新审视Shor的量子算法用于计算一般的离散对数

Revisiting Shor's quantum algorithm for computing general discrete logarithms

本文重新审视Shor算法，通过改进半经典傅里叶变换实现高效计算，通过增加量子操作和经典后处理搜索，使算法成功概率超过99%。

The quantum mechanics based on a general kinetic energy

In this paper, we introduce the Schrodinger equation with a general kinetic energy operator. The conservation law is proved and the probability continuity equation is deducted in a general sense. Examples with a Hermitian kinetic energy operator include the standard Schrodinger equation, the relativistic Schrodinger equation, the fractional Schrodinger equation, the Dirac equation, and the deformed Schrodinger equation. We reveal that the Klein-Gordon equation has a hidden non-Hermitian kinetic energy operator. The probability continuity equation with sources indicates that there exists a diff…

从基本原理导出薛定谔方程

Derivation of the Schrodinger equation from fundamental principles

本文基于概率幅的物理意义和能量动量关系，推导出薛定谔方程，解决了传统方法中依赖物理直觉而非形式推导的问题。

Revisiting Zeno's paradox: Flying arrows for atom-diatom reactions

The possibility to observe quantum Zeno and anti-Zeno scenarios for atom-diatom reactive collisions is investigated for two diferent processes (F+HD and H+O_2) by means of time-dependent wave packet propagations. A novel approach is proposed in which the survival probabilities investigated are those obtained when the initial state is redefined after time intervals tau at which measurements are performed on the system. The comparison with the actual probability for the unperturbed system reveals the existence of a regime in which the decay from the initial state appears to be inhibited (the qua…

Time Evolution and Probability in Quantum Theory: The Central Role of Born's Rule

In this treatise I introduce the time dependent Generalized Born's Rule for the probabilities of quantum events, including conditional and consecutive probabilities, as the unique fundamental time evolution equation of quantum theory. Then these probabilities, computed from states and events, are to be compared with relative frequencies of observations. Schrodinger's equation still is valid in one model of the axioms of quantum theory, which I call the Schrodinger model. However, the role of Schrodinger's equation is auxiliary, since it serves to help compute the continuous temporal evolution …

Generalized probability and current densities: A field theory approach

We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schrodinger equation. The extended probability and particle current densities are found which satisfy the continuity equation.