Quantum mechanics in q-deformed calculus

Starting on the basis of q-deformed calculus and q-symmetric oscillator algebra, we introduce a generalized Schrodinger equation which admits factorized time-space solutions and the free plane wave functions can be expressed in terms of the so-called basic-hypergeometric functions. In this framework, q-deformed adjoint and q-hermitian operator properties occur in a natural way in order to satisfy the fundamental quantum mechanics assumptions.