Erratum to: Canonical coherent states for the relativistic harmonic oscillator
V. Aldaya, J. Guerrero
在J.Math.Phys.36，3191（1995）中对$\hatκ$的表达是错误的。给出了正确的表达式。
The expression for $\hatκ$ in J. Math. Phys. 36, 3191 (1995) was miswritten. The correct expression is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
The Weyl algebra,- the usual C*-algebra employed to model the canonical commutation relations (CCRs), has a well-known defect in that it has a large number of representations which are not regular and these cannot model physical fields. Here, we construct explicitly a C*-algebra which can reproduce the CCRs of a countably dimensional symplectic space (S,B) and such that its representation set is exactly the full set of regular representations of the CCRs. This construction uses Blackadar's version of infinite tensor products of nonunital C*-algebras, and it produces a "host algebra" (i.e. a ge…
We consider a class of perturbations of the 2D harmonic oscillator, and of some other dynamical systems, which we show are isomorphic to a function of a toric system (a Birkhoff canonical form). We show that for such systems there exists a quantum normal form as well, which is determined by spectral data.
We calculate the susceptibility of a canonical ensemble of quantum oscillators to the singular random metric. If the covariance of the metric is $\vert {\bf x}-{\bf x}^{\prime}\vert^{-4α}$ $0< α<\frac{1}{2}$ then the expansion of the partition function in powers of the temperature involves non-integer indices.
The Wigner distribution function for the one-dimensional parabose oscillator
在20世纪50年代初，维格纳从正则量子力学谐振子引入了一个基本变形，现在有时称为维格纳量子振荡器或抛物面振荡器。此外，在量子力学中，所谓的维格纳分布被认为是相空间上经典概率分布的最接近的量子模拟。在这篇文章中，我们考虑了在非正则量子力学的情况下，这种分布函数的定义可以使用。然后，我们明确地计算两个不同的表达式，这个分布函数的情况下的抛物面振荡器。这两个表达式原来是多个总和涉及（广义）拉盖尔多项式。曲线图表明抛物面振子基态的维格纳分布函数与正则量子振子第一激发态的维格纳分布函数的行为相似。
Canonical equivalence of a charge in a time dependent, spatially-homogeneous electromagnetic field to a time-dependent perturbed oscillator
本文证明了静态或时变空间均匀电磁场中的粒子系统在规范和酉上等价于受微扰的谐振子，通过复合变换可积分初始问题，并指出其本征态表现为谐振子的纠缠态。
The main goal of this work is to study the Dirac oscillator as a quantum field using the canonical formalism of quantum field theory and to develop the canonical quantization procedure for this system in $(1+1)$ and $(3+1)$ dimensions. This is possible because the Dirac oscillator is characterized by the absence of the Klein paradox and by the completeness of its eigenfunctions. We show that the Dirac oscillator field can be seen as constituted by infinite degrees of freedom which are identified as decoupled quantum linear harmonic oscillators. We observe that while for the free Dirac field th…
Canonical Discretization. I. Discrete faces of (an)harmonic oscillator
提出了量子力学中的正则等价概念。它用于将量子系统与离散系统联系起来。找到了与著名谐振子正则等价的离散系统以及四次和拟精确可解的非谐振子，它们可以看作是谐振子保等谱的离散协变离散化.还提出了正则等价的$q-$变形的概念，从而导致保持特征函数多项式性的离散化协变。
d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass
本文描述了薛定谔方程中质量依赖于位置的量子粒子的点正则变换的d维推广。示例包括：以谐振子、库仑势、尖峰谐振子、Kratzer势、Morse势、Poschl-Teller势和Hulthen势为参考势，得到了不同位置质量设置下靶势的精确能量本征值和本征函数.
A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally, the discrete spectrum of the corresponding deformed harmonic oscillator Hamiltonian is investigated and discussed.
Graded extension of SO(2,1) Lie algebra and the search for exact solutions of Dirac equation by point canonical transformations
SO（2，1）是一类三参数问题的对称代数，包括振子、库仑势和Morse势以及其他零能量问题。这类势都可以通过点正则变换映射到振子势。我们称这个类为“振荡器类”。定义了SO（2，1）的一个非平凡分次扩张，并给出了它在旋量空间中的二维微分算子矩阵的实现。结果表明，这个分次代数是一类相对论势的超对称代数，这类势包括Dirac-振子势、Dirac-库仑势和Dirac-Morse势。这个类实际上是振子类的相对论性扩展。提出了一种新的与相对论问题相容的点正则变换。它将所有这些相对论性势映射到狄拉克-振子势。
In this work we address the problem of the quantization of a simple harmonic oscillator that is perturbed by a time dependent force. The approach consists of removing the perturbation by a canonical change of coordinates. Since the quantization procedure uses the classical Hamiltonian formalism as staring point, the change of variables is carried out using canonical transformations, and to transform between the quantized systems the canonical transformation is implemented as a unitary transformation mapping the states of the perturbed and unperturbed system onto each other.
Quantization of Damped Harmonic Oscillator, Thermal Field Theories and q-Groups
利用Weyl-Heisenberg代数（q-WH）的q-变形在有限差分算子中的实现，研究了阻尼谐振子的正则量子化.我们将阻尼振子哈密顿量与q-WH代数和相干态理论的压缩生成元联系起来。我们还表明，q-WH代数是研究热场论的自然候选者。本文结合量子力学中的冯·诺依曼定理和q-WH代数，对在无限体积极限下物理状态空间分裂成正则对易关系的幺正不等价表示这一著名现象作了简要评论。
The quantum oscillator and Kepler-Coulomb problems in $d$-dimensional spaces with constant curvature are analyzed from several viewpoints. In a deformed supersymmetric framework, the corresponding nonlinear potentials are shown to exhibit a deformed shape invariance property. By using the point canonical transformation method, the two deformed Schrödinger equations are mapped onto conventional ones corresponding to some shape-invariant potentials, whose rational extensions are well known. The inverse point canonical transformations then provide some rational extensions of the oscillator and Ke…
In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case. In this paper, we take a more general approach and look at the system as a Wigner quantum system. Hereby, one does not assume the canonical commutation relations, but instead one just requires the compatibility between the Hamilton and Heisenberg equations. Solutions of this problem are related to the Lie superalgebras gl(1|n) and osp(1|2n). We determine the …
Our purpose in this paper is to analyze the Pais-Uhlenbeck (PU) oscillator using complex canonical transformations. We show that starting from a Lagrangian approach we obtain a transformation that makes the extended PU oscillator, with unequal frequencies, to be equivalent to two standard second order oscillators which have the original number of degrees of freedom. Such extension is provided by adding a total time derivative to the PU Lagrangian together with a complexification of the original variables further subjected to reality conditions in order to maintain the required number of degree…
We construct a new class of coherent states indexed by points z of the complex plane and depending on two positive parameters m and epsilon by replacing the coefficients of the canonical coherent states by polyanalytic functions. These states solve the identity of the states Hilbert space of the harmonic oscillator at the limit epsilon goes to zero and obey a thermal stability property. Their wavefunctions are obtained in a closed form and their associated Bargmann-type transform is also discussed.
Impact of the non-canonical approach to the exact solution of the ideal one-dimensional electron gas confined with an anisotropic quantum wire of oscillator-shaped profile
研究了一个可解模型，探讨了各向异性量子线势形如振子形状对理想一维电子气的影响，通过标准和非标准方法求解，并得到波函数和能谱的解析表达式。
The phase coordinates transformation in Moyal noncommutative framework 2-dimensional harmonic oscillator and Painlevé second equation
本文通过Moyal非交换相坐标变换构造二维谐振子与Painlevé第二方程的非交换类比，揭示额外对称性并生成Yablonskii-Vorobev多项式。
We construct a new class of coherent states labeled by points z of the complex plane and depending on three numbers (gamma, nu) and epsilon positive by replacing the coefficients of the canonical coherent states by Laguerre polynomials. These states are superpositions of eigenstates of the symmetric Poschl-Teller oscillator and they solve the identity of the states Hilbert space at the limit epsilon goes to 0. Their wavefunctions are obtained in a closed form for a special case of parameters (gamma, nu). We discuss their associated coherent states transform which leads to an integral represent…
We construct a class of generalized phase coherent states indexed by points of the unit circle and depending on three positive parameters "gamma","alpha" and "epsilon" by replacing the labelling coefficients of the canonical coherent states by circular Jacobi polynomials with parameter "gamma". The special case "gamma" = 0 corresponds to well known phase coherent phase states. The constructed states are superposition of eigenstates of a one-parameter pseudoharmonic oscillator depending on "alpha" and solve the identity of the state Hilbert space at the limit "epsilon"->0+. Closed form for thei…
The study of the symmetry of Pais-Uhlenbeck oscillator initiated in [Nucl. Phys. B 885 (2014) 150] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton-Hooke algebra. In this important cas…
We construct two-parameters family of nonlinear coherent states by replacing the factorial in coefficients $z^n/\sqrt{n!}$ of the canonical coherent states by a specific generalized factorial $x_n^{γ,σ}!$ where parameters $γ$ and $σ$ satisfy some conditions for which the normalization condition and the resolution of identity are verified. The obtained family is a generalization of the Barut-Girardello coherent states and those of the philophase states. In the particular case of parameters $γ$ and $σ$, we attache these states to the pseudo-harmonic oscillator depending on two parameters $α,β> 0…
Performing the Hamiltonian analysis we explicitly established the canonical equivalence of the deformed oscillator, constructed in arXiv:1607.03756[hep-th], with the ordinary one. As an immediate consequence, we proved that the SU(1,2) symmetry is the dynamical symmetry of the ordinary two-dimensional oscillator. The characteristic feature of this SU(1,2) symmetry is a non-polynomial structure of its generators written it terms of the oscillator variables.
We consider a one-parameter family of nonlinear coherent states by replacing the factorial in coefficients of the canonical coherent states by a specific generalized factorial depending on a parameter gamma. These states are superposition of eigenstates of the Hamiltonian with a symmetric Poschl-Teller potential depending on a parameter nu > 1. The associated Bargmann-type transform is defined for equal parameters. Some results on the infinite square well potential are also derived. For some different values of gamma, we discuss two sets of orthogonal polynomials that are naturally attached to…
In a recent paper by Jafarov, Nagiyev, Oste and Van der Jeugt (2020 {\sl J.\ Phys.\ A} {\bf 53} 485301), a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent on the position, was constructed and it was shown that the confinement parameter gets quantized. By using a point canonical transformation starting from the constant-mass Schrödinger equation for the Rosen-Morse II potential, it is shown here that similar results can be easily obtained without quantizing the confinement parameter. In addition, an extension t…
In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. Here, after a two-dimensional extension of the general framework, we apply the theory to a generalized version of the two-dimensional Hamiltonian describing Landau levels. Moreover, for this system, we discuss coherent states and we deduce a resolution of the identity. We also consider a diffe…
Zernike system revisited: imaginary gauge and Higgs oscillator
本文重新审视Zernike系统，通过规范变换将其等价于Higgs振子，揭示其在不同参数下的量子行为。
We apply the Dirac factorization method to the nonrelativistic harmonic oscillator and, more in general, to Hamiltonians with a generic potential. It is shown that this procedure naturally leads to a supersymmetric formulation of the problems under study. It is also speculated on the physical meaning underlying this method and it is suggested that the vacuum field fluctuations can be viewed as the spontaneous emission of the associated two-level system, whose quantization is due to the noncommuting nature of the harmonic oscillator canonical variables.
A Perturbative Approach to the Relativistic Harmonic Oscillator
用空间变量$x$和${\d\over \d x}$（最小正则表象）实现了相对论谐振子的量子实现。通过在常数$c^{-1}$中使用微扰展开，找到了哈密顿算符的本征态（在低阶）。与相对论性氢原子的Foldy-Wouthuysen变换版本不同，传统的微扰理论不能应用，而需要对标量积本身进行微扰。
Rationally-extended radial harmonic oscillator in a position-dependent mass background
本文通过点规范变换将具有位置依赖质量的径向谐振子问题转化为Pöschl-Teller I势问题，并利用X_m-雅可比例外正交多项式提出精确可解的有理扩展。
We apply the Born-Jordan and Weyl quantization formulas for polynomials in canonical coordinates to the constants of motion of some examples of the superintegrable 2D anisotropic harmonic oscillator. Our aim is to study the behaviour of the algebra of the constants of motion after the different quantization procedures. In the examples considered, we have that the Weyl formula always preserves the original superintegrable structure of the system, while the Born-Jordan formula, when producing different operators than the Weyl's one, does not.
We introduce a $d$-dimensional system of charged harmonic oscillators in a magnetic field perturbed by a stochastic dynamics which conserves energy but not momentum. We study the thermal conductivity via the Green-Kubo formula, focusing on the asymptotic behavior of the Green-Kubo integral up to time $t$ (i.e., the integral of the correlation function of the total energy current). We employ the microcanonical measure to calculate the Green-Kubo formula in general dimension $d$ for uniformly charged oscillators. We also develop a method to calculate the Green-Kubo formula with the canonical mea…
Non-symplectic symmetries and bi-Hamiltonian structures of the rational Harmonic Oscillator
利用几何对称性理论分析了有理谐振子（具有有理频率比的非中心谐振子）双哈密顿结构的存在性。我们证明，这些额外的结构是一个后果的存在的动力学对称的非辛（非规范）型。同时也得到了相应的递归算子。
Deformation of the Heisenberg-Weyl algebra and the Lie superalgebra $\mathfrak{osp}\left( {1|2} \right)$: exact solution for the quantum harmonic oscillator with a position-dependent mass
本文通过引入位置依赖质量对 Heisenberg-Weyl 代数进行形变，精确求解了量子谐振子问题，并将其推广到李超代数 osp(1|2) 下的 parabose 谐振子，揭示了形变后能谱仍等间距但波函数由 Hermite 多项式变为 Laguerre 多项式的规律。
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat noncommutative space and employ it to study the eigenvalue spectrum for the harmonic oscillator on this space. The perturbative expression for the eigenenergy indicates that the model might possess an exceptional point at which the spectrum becomes complex and its PT-symmetry is spontaneously broken.
In this paper, a new approach for constructing Lagrangians for driven and undriven linearly damped systems is proposed, by introducing a redefined time coordinate and an associated coordinate transformation to ensure that the resulting Lagrangian satisfies the Helmholtz conditions. The approach is applied to canonically quantize the damped harmonic oscillator and although it predicts an energy spectrum that decays at the same rate to previous models, unlike those approaches it recovers the classical critical damping condition, which determines transitions between energy eigenstates, and is the…
We prove that Gibbs measures based on 1D defocusing nonlinear Schr{ö}dinger functionals with sub-harmonic trapping can be obtained as the mean-field/large temperature limit of the corresponding grand-canonical ensemble for many bosons. The limit measure is supported on Sobolev spaces of negative regularity and the corresponding density matrices are not trace-class. The general proof strategy is that of a previous paper of ours, but we have to complement it with Hilbert-Schmidt estimates on reduced density matrices.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。