Basic-deformed quantum mechanics

Starting on the basis of q-symmetric oscillator algebra and on the associated q-calculus properties, we study a deformed quantum mechanics defined in the framework of the basic square-integrable wave functions. In this context, we introduce a deformed Schrödinger 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.