Propriedades termodinâmicas em sistemas quânticos com massa dependente da posição

Abstract

In this work, in possession of an analytical solution of the one-dimensional energy spectrum of a free particle with position-dependent mass, in a thermal bath, we discuss the thermodynamic properties and find that for high temperatures the average energy and the specific heat obey the equipartition theorem. Then, taking advantage of this analytical expression of the full energy spectrum, we analyze the exact summation of the conventional partition function. With this, we obtain a solution for any temperature with dependence on Jacobi’s theta function. Thus, we obtain analytical expressions for the following thermodynamic quantities: entropy, Helmholtz free energy, average energy and specific heat at constant volume.