Fermi energy in the q-deformed quantum mechanics

Abstract

In this paper, we use the q-derivative emerging in the non-extensive statistical physics to formulate the q-deformed quantum mechanics. We find the algebraic structure related to this deformed theory and investigate some properties of the q-deformed elementary functions. Using this mathematical background, we formulate the q-deformed Heisenberg algebra and q-deformed time-dependent Schrodinger equation. As an example, we deal with the infinite potential well and compute the Fermi energy in the q-deformed theory.