  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.
