Temperature: The ignored factor in quantum mechanics
Abstract
We have developed a theoretical formalism to introduce temperature as a parameter into the framework of non-relativistic quantum mechanics using the laws of classical thermodynamics and the canonical ensemble scheme of statistical mechanics. A self-consistent Hamiltonian has then been constructed for a given quantum many-body system which includes the effect of temperature in the form of correction terms added to the corresponding zero-temperature Hamiltonian of the system. Investigating some quantum mechanical systems with exact zero-temperature solutions including the particle-in-a-box model, the free particle, and the harmonic oscillator within our finite-temperature approach up to the first order of self-consistency has led to temperature-dependent Hamiltonians describing these systems above absolute zero without encountering any physically unacceptable brand of behavior for their wave functions and energy spectra. Results firmly support the view that a quantum mechanical system at a finite temperature behaves as if it is in a zero-temperature excited state.
Cite
@article{arxiv.2001.05212,
title = {Temperature: The ignored factor in quantum mechanics},
author = {Ashkan Shekaari and Mahmoud Jafari},
journal= {arXiv preprint arXiv:2001.05212},
year = {2021}
}
Comments
In fact, according to the comments we received from other researchers of the field, and based on our further investigation, and more importantly by taking into account the arXiv's advice regarding the way to update and make corrections to articles, we manipulated and improved some parts of our previous manuscript in order to be more rigorous in content and more illustrative in presentation