Quantum Mechanics in the general quantum systems (VI): exact series solution of stationary Schr\"odinger's equation

TL;DR

This paper presents an exact series solution to the stationary Schrödinger equation for general quantum systems, avoiding approximations and including all perturbative contributions, with practical and theoretical applications.

Contribution

It introduces a complete, exact series solution for the stationary Schrödinger equation applicable to general quantum systems, along with new expressions for the Green operator.

Findings

Provides an exact series solution without approximations

Includes all perturbation contributions in the solution

Offers useful forms of the solution and Green operator

Abstract

We obtain a complete series solution of stationary Schr\"odinger's equation in the general quantum systems. It is exact in the sense that any approximation means is not used, or that the whole corrections or contributions from all order perturbations are involved if the perturbation concept is introduced. Furthermore, the useful forms of our exact solution and a new expression the complete Green operator are given out. As a universal and analytical solution, it is helpful for the theoretical derivations and practical calculations in quantum theory.