Correspondence Between Classical and Quantum Theory by $f$-Deformed Coherent State

TL;DR

This paper introduces an $f$-deformed coherent state framework within deformation quantization, defining a new $f$-star product to exactly determine the spectrum of deformed quantum systems.

Contribution

It presents a novel $f$-star product and an ${}$-eigenvalue equation, enabling exact spectral analysis of deformed Hamiltonians in quantum mechanics.

Findings

Defined a new $f$-star product for deformation quantization.

Derived an exact spectrum calculation method for deformed systems.

Established a correspondence between classical and quantum $f$-deformed states.

Abstract

Generalized $f$-coherent state approach in deformation quantization framework is investigated by using a $\ast $-eigenvalue equation. For this purpose we introduce a new Moyal star product called $f$-star product, so that by using this ${\ast}_{f}$-eigenvalue equation one can obtain exactly the spectrum of a general Hamiltonian of a deformed system.