TL;DR
This paper develops a version of quantum mechanics based on q-deformed algebra and calculus, introducing a deformed Schrödinger equation with solutions expressed via q-exponentials, expanding the mathematical framework of quantum theory.
Contribution
It introduces a deformed Schrödinger equation within a q-deformed algebraic framework, utilizing basic hypergeometric functions for solutions.
Findings
Deformed Schrödinger equation consistent with quantum principles
Plane wave solutions expressed with q-exponentials
Framework extends quantum mechanics with q-deformed mathematical structures
Abstract
Starting on the basis of -symmetric oscillator algebra and on the associate -calculus properties, we study a deformed quantum mechanics defined in the framework of the basic square-integrable wave functions space. In this context, we introduce a deformed Schroedinger equation, which satisfies the main quantum mechanics assumptions and admits, in the free case, plane wave functions that can be expressed in terms of the q-deformed exponential, originally introduced in the framework of the basic-hypergeometric functions.
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