Temperature: The ignored factor in quantum mechanics
- URL: http://arxiv.org/abs/2001.05212v2
- Date: Thu, 4 Mar 2021 19:08:09 GMT
- Title: Temperature: The ignored factor in quantum mechanics
- Authors: Ashkan Shekaari and Mahmoud Jafari
- Abstract summary: We introduce temperature as a parameter into the framework of non-relativistic quantum mechanics.
We investigate some quantum mechanical systems with exact zero-temperature solutions.
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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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