2021/03/04 by Shekaari, Ashkan, Jafari, Mahmoud
#FOS: Physical sciences #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2103.03306
The perturbative approach was adopted to develop a temperature-dependent version of non-relativistic quantum mechanics in the limit of low-enough temperatures. A generalized, self-consistent Hamiltonian was therefore constructed for an arbitrary quantum-mechanical system in a way that the ground-state Hamiltonian turned out to be just a limiting case at absolute zero. The weak-coupling term connecting the system of interest and its immediate environment was accordingly treated as the perturbation. Applying the obtained generalized Hamiltonian to some typical quantum systems with exact zero-temperature solutions, including the free particle in a box, the free particle in vacuum, and the harmonic oscillator, up to the first order of self-consistency, therefore corrected their associated Hamiltonians, energy spectrums, and wavefunctions to be consistent with the low-temperature limit. Further investigation revealed some kind of quantum tunneling effect by a residual probability for the free particle in a box, as a chief consequence of thermally coupling to the reservoir. The possible effects of thermal environment on the main properties of the wavefunctions were also thoroughly examined and discussed.