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 (20)

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Cited by in corpus (15)

• Nonextensive statistical effects in the quark-gluon plasma formation at relativistic heavy-ion collisions energies
• A position-dependent mass harmonic oscillator and deformed space
• Thermostatistics of deformed bosons and fermions
• Intermediate statistics as a consequence of deformed algebra
• Basic-deformed quantum mechanics
• Scattering theory using smeared non-Hermitian potentials
• Nonextensive statistical effects in the hadron to quark-gluon phase transition
• Thermal and electrical properties of a solid through Fibonacci oscillators
• Deformed quantum statistics in two-dimensions
• Fibonacci Oscillators in the Landau Diamagnetism problem
• q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials
• Enhancement of nonclassical properties of two qubits via deformed operators
• Non-Archimedean Quantum Mechanics via Quantum Groups
• The q-Gauss-Newton method for unconstrained nonlinear optimization
• Wigner distribution function of atomic system interacts locally with a deformed cavity