Non-relativistic quantum theory at finite temperature

TL;DR

This paper introduces non-relativistic quantum wave equations at finite temperature, exploring how temperature affects energy levels, eigenfunctions, and transition frequencies in single and multiple particle systems.

Contribution

It presents new finite temperature quantum wave equations and analyzes the relationship between energy eigenvalues, transition frequencies, and temperature effects.

Findings

Transition frequency remains unchanged when degeneracies are equal despite temperature changes.

Variance in transition frequency is proportional to temperature difference when degeneracies differ.

Provides theoretical insights into temperature effects on quantum energy transitions.

Abstract

We propose the non-relativistic finite temperature quantum wave equations for a single particle and multiple particles. We give the relation between energy eigenvalues, eigenfunctions, transition frequency and temperature, and obtain some results: (1) when the degeneracies of two energy levels are same, the transition frequency between the two energy levels is unchanged when the temperature is changed. (2) When the degeneracies of two energy levels are different, the variance of transition frequency at two energy levels is direct proportion to temperature difference.