Deformed quantum mechanics and q-Hermitian operators

Details Deformed quantum mechanics and q-Hermitian operators Deformed quantum mechanics and q-Hermitian operators

2008-08-14

arxiv.org/abs/0808.1976v1

J. Phys. A: Math. Theor. 41 (2008) 244014

Physics

Mathematical Physics

10 pages

Scientific paper

10.1088/1751-8113/41/24/244014

Starting on the basis of the non-commutative q-differential calculus, we introduce a generalized q-deformed Schr\"odinger 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.

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