A remarkable property of the Schrödinger equation. (English) Zbl 0862.70014
Summary: We consider the Schrödinger equation written for a discrete conservative system. We demonstrate the following property: if the Hamilton-Jacobi equation for this system has a periodic solution, the values of the total energy which result from the Schrödinger equation can be rigorously calculated by line integrals of analytical functions. This property leads to a simplification of the modelling of discrete systems.
MSC:
70H20 | Hamilton-Jacobi equations in mechanics |
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |