Classical limit of scattering in quantum mechanics—A general approach

The classical and quantum physics seem to divide nature into two domains macroscopic and microscopic. It is also certain that they accurately predict experimental results in their respective regions. However, the reduction theory, namely, the general derivation of classical results from the quantum mechanics is still a far cry. The outcome of some recent investigations suggests that there possibly does not exist any universal method for obtaining classical results from quantum mechanics. In the present work we intend to investigate the problem phenomenonwise and address specifically the phenomenon of scattering. We suggest a general approach to obtain the classical limit formula from the phase shiftδ _l, in the limiting value of a suitable parameter on whichδ _l depends. The classical result has been derived for three different potential fields in which the phase shifts are exactly known. Unlike the current wisdom that the classical limit can be reached only in the high energy regime it is found that the classical limit parameter in addition to other factors depends on the details of the potential fields. In the last section we have discussed the implications of the results obtained.     

New WKB method in supersymmetry quantum mechanics

In this paper, we combine the perturbation method in supersymmetric quantum mechanics with the WKB method to restudy an angular equation coming from the wave equations for a Schwarzschild black hole with a straight string passing through it. This angular equation serves as a naive model for our investigation of the combination of supersym- metric quantum mechanics and the WKB method, and will provide valuable insight for our further study of the WKB approximation in real problems, like the one in spheroidal equations, etc.     

关于量子力学中态叠加原理的讨论

讨论了量子力学中态叠加原理的意义,评论了它的不同表述和解说,并且以简单明了的语言来叙述这一原理．     

The Wigner function in the relativistic quantum mechanics

A detailed study is presented of the relativistic Wigner function for a quantum spinless particle evolving in time according to the Salpeter equation.     

Maximally causal quantum mechanics

We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics     

Quantum cards and quantum rods

Quantum mechanical analysis of a rigid rod with one end fixed to a flat table is presented. Assuming that the rod is initally in the upright orientation, “the time of fall” is calculated using WKB wavefunctions representing energy eigenstates near the barrier summit.      

Langevin formulation of quantum mechanics

Summary We present in a rather pedagogical way a new formulation of quantum mechanics. Our starting point is the path integral representation of the quantum-mechanical propagator analytically continued to imaginary timeW(X″, s″|X′, s′). We view the set of random paths contributing toW(X″, s″|X′, s′) as the manifold of solutions of a Langevin equation with a Gaussian white noise. We thus obtainW(X″, s″|X′, s′) as the noise-average of a suitable functional of the solution of the Langevin equation. The standard quantum-mechanical propagator is finally recovered by analytically continuingW(X″, s″|X′, s′) back to real time. The present approach allows for a straightforward application of standard methods of classical stochastic processes to quantum-mechanical problems and offers a new promising way to perform computer simulations of quantum-dynamical systems. To speed up publication, the author has agreed not to receive proofs which have been supervised by the Scientific Committee.     

量子力学虚拟实验的MATLAB演示

量子力学是一门较抽象的科学.为了更直观、形象地展示量子力学中的一些物理原理和实验现象,本文利用MAT-LAB软件搭建了一个量子力学的虚拟演示平台,可以生动地演示电子双缝衍射、量子隧穿效应、氢原子电子云和斯塔克效应等现象.通过相关物理参数的输入以及物理现象的演示,可以使学生在量子力学的学习中获得更直观的教学感受.     

Supersymmetric quantum mechanics and the index theorem

We consider the classical mechanics of the spinning particle and investigate which Abelian interactions can be added without breaking supersymmetry. A quantum theory is presented. The well known index theorem for the Dirac operator is extended to take into account the effect of anti-symmetric Abelian tensor fields. Furthermore interactions with non-Abelian anti-symmetric tensor fields are investigated. It turns out in both cases that these fields do not give any non-trivial contributions to the index.     

递推与迭代在量子力学近似计算中的应用

综述了非简并微扰论和简并微扰论的递推形式，一维阶梯位势透射系数的递推计算及变化法的迭代形式，在给定的精度下，利用上述方法可以得到与精确解完全一致的效果。     

q-Deformation of algebraic structures of quantum and classical mechanics

There exists a coassociative and cocommutative coproduct in the linear space spanned by the two algebraic products of a classical Hamilton algebra (the algebraic structure underlying classical mechanics [1]). The transition from classical to quantum Hamilton algebra (the algebraic structure underlying quantum mechanics) is anħ-deformation which preserves not only the Lie property of the classical Hamilton algebra but also the coassociativity and cocommutativity of the above coproduct. By explicit construction we obtain the algebraic structures of theq-deformed Hamilton algebras which preserve the said properties of the coproduct. Some algorithms of these structures are obtained and their implications discussed. The problem of consistency of time evolution with theq-deformed kinematical structure is discussed. A characteristic distinction between the parametersħ andq is brought out to stress the fact thatq cannot be regarded as a fundamental constant.     

量子力学基本概念教学探讨

用一维无限深势阱中粒子的动态量子模型讨论了态叠加原理和时间与能量的不确定关系原理的意义,指出量子隧穿效应静态模型的疑难,建立了一个隧穿效应动态模型,并讨论了隧穿效应的微观机制.     

The logic of quantum mechanics derived from classical general relativity

For the first time it is shown that the logic of quantum mechanics can be derived from classical physics. An orthomodular lattice of propositions characteristic of quantum logic, is constructed for manifolds in Einstein’s theory of general relativity. A particle is modelled by a topologically non-trivial 4-manifold with closed timelike curves—a 4-geon, rather than as an evolving 3-manifold. It is then possible for both the state preparationand measurement apparatus to constrain the results of experiments. It is shown that propositions about the results of measurements can satisfy a non-distributive logic rather than the Boolean logic of classical systems. Reasonable assumptions about the role of the measurement apparatus leads to an orthomodular lattice of propositions characteristic of quantum logic.     

关于量子力学的基本原理

文章抽选关于量子力学基本原理的几个题目,包括量子力学与经典物理学的对比、量子概念的产生、薛定谔方程的出现、全同性原理和量子路径积分等,作些说明。目的在于激发读者思考量子力学的本质在哪里。     

Kink mass quantum shifts from SUSY quantum mechanics

In this paper a new version of the DHN (Dashen–Hasslacher–Neveu) formula, which is used to compute the one-loop order kink mass correction in (1+1)-dimensional scalar field theory models, is constructed. The new expression is written in terms of the spectral data coming from the supersymmetric partner operator of the second-order small kink fluctuation operator and allows us to compute the kink mass quantum shift in new models for which this calculation was out of reach by means of the old formula.