论文标题
Schroedinger方程和非惯性框架中相关的物理
Schroedinger Equation and the Associated Physics in Non-Inertial Frame
论文作者
论文摘要
在本文中，我们开发了一种形式主义，以在非惯性框架中获得Schroedinger方程的解决方案。该框架相对于具有加速度的惯性框架移动。如Landau和Lifshitz的古典力学书中所讨论的，使用拉格朗日形式主义开发了该公式。因此，我们获得了核子的哈密顿量。然后，使用规范量化规则的标准形式，我们在非惯性框架中设置了Schroedinger方程。在本研究中，我们仅考虑了非惯用框架的加速直线运动。基于量子场理论[2]的一些未来工作中，将考虑旋转（另见[3，4]）。因此，我们在计算中放下了哈密顿量的旋转部分。我们工作的物理上可接受的结果基本上是Fowler和Nordheim获得的解决方案，从而从强电场诱导的冷金属表面发射电子[5]，称为电子的冷场发射。然而，在目前的公式中，重力作用于粒子的质量并引起发射。离心力的作用就像重力。因此，在我们的非相关方法的有限范围内，我们有一些霍金辐射的风味[6]，也具有iNRUH效应[7]。我们还表明，两个身体量子机械系统的相对运动不取决于参考框架的性质。
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.
