Abstract
This study investigates the quantum mechanics of the harmonic oscillator in the presence of the Generalised-Wigner–Dunkl formalism based on creation and annihilation operators, which include also the reflection operator. We provide explicit results on the spectral properties of the Hamiltonian and an explicit form of the quantum propagator. Deformed coherent states are introduced and their non-classical properties such as photon statistics, Mandel parameter, and bunching or anti-bunching effect are studied.
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