非惯性系中的薛定谔方程及其相关物理
Schroedinger Equation and the Associated Physics in Non-Inertial Frame
摘要：
本文给出了非惯性系中薛定谔方程的一种形式。该坐标系相对于惯性坐标系以加速度运动。该公式是使用拉格朗日形式主义发展的，正如Landau和Lifshitz [1]在经典力学书中所讨论的那样。因此我们得到了核子的哈密顿量。然后利用正则量子化定则的标准形式，建立了非惯性系中的薛定谔方程。在本研究中，我们只考虑了非惯性系中的加速直线运动。旋转将在基于量子场论的一些未来工作中考虑[2]（也见[3，4]）。因此，我们在计算中去掉了哈密顿量的旋转部分。我们工作中物理上可接受的结果基本上是Fowler和Nordheim对强电场[5]引起的冷金属表面电子发射（称为冷场电子发射）所获得的解。然而，在本公式中，是重力作用于颗粒的质量并引起发射。离心力的作用类似于重力。因此，在我们的非相对论方法的有限范围内，我们得到了霍金辐射[6]和Unruh效应[7]的一些结果。我们还证明了两体量子力学系统的相对运动不取决于参考系的性质。
英文摘要：
In this article we have developed a formalism to obtain the solution of Schroedinger equation in a non-inertial frame. The frame is moving relative to an inertial frame with an acceleration. The formulation has been developed using Lagrangian formalism as discussed in Classical Mechanics book by Landau and Lifshitz [1]. Hence we have obtained the Hamiltonian of the nucleons. Then using the standard form of canonical quantization rule, we have setup the Schroedinger equation in non-inertial frame. In the present study we have considered only the accelerated rectilinear motion of the non-inertial frame. The rotation will be considered in some future work based on quantum field theory [2] (see also [3, 4]). We therefore drop the rotation part of the Hamiltonian in our calculation. The physically acceptable result on our work is basically the solution obtained by Fowler and Nordheim for the emission of electrons from cold metal surface induced by strong electric field [5] known as cold field emission of electrons. However in the present formulation, it is the gravity which acts on mass of the particle and causes emission. The centrifugal force acts like gravity. Hence we have got some flavor of Hawking radiation [6] and also Unruh effect [7] within the limited scope of our non-relativistic approach. We have also shown that relative motion of a two body quantum mechanical system does not depend on the nature of the frame of reference.
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