The q-deformed Schrödinger equation based on the q-map: one dimensional case

Abstract

In this paper, we adopt q-deformed binary operations, such as q-addition, q-subtraction, q-multiplication, and q-division, to construct the q-deformed Schrödinger equation in one dimension. We explore the mathematics involving q-deformed binary operations. We q-deform the ordinary commutator and the definition of Fock space in q-deformed quantum mechanics. As examples, we discuss the particle in a box and the harmonic oscillator. © The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024.