Deformed quantum mechanics and q-Hermitian operators

Abstract

Starting on the basis of the non-commutative q-differential calculus, we introduce a generalized q-deformed Schrödinger equation. It can be viewed as the quantum stochastic counterpart of a generalized classical kinetic equation, which reproduces at the equilibrium the well-known q-deformed exponential stationary distribution. In this framework, q-deformed adjoint of an operator and q-hermitian operator properties occur in a natural way in order to satisfy the basic quantum mechanics assumptions.

10 pages

References in corpus (4)

• Faster than Hermitian Quantum Mechanics
• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
• Basic-deformed thermostatistics
• Classical and quantum q-deformed physical systems

Cited by in corpus (1)

• Scattering theory using smeared non-Hermitian potentials