New $\mathcal {SU}(1,1)$ position-dependent effective mass coherent states for a generalized shifted harmonic oscillator

Abstract

A new position-dependent effective mass coherent states (PDEM CS) related to the shifted harmonic oscillator (SHO) are deduced. This is accomplished by applying a similarity transformation to the generally deformed oscillator algebra (GDOA) generators for PDEM systems and a new set of operators that close the Lie algebra are constructed, being the PDEM CS of the basis for its unitary irreducible representation. From the Lie algebra generators, we evaluate the uncertainty relationship for a position and momentum-like operators in the PDEM CS and show that it is minimized in the sense of Barut–Girardello CS. We prove that the deduced PDEM CS preserve the same analytical form than those of Glauber states. As an illustration of our procedure, we depicted the 2D-probability density in the PDEM CS for SHO with the explicit form of the mass distribution with no singularities.

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“…Its main characteristic is that the conventional expression for the kinetic termp 2 2m is not self-adjoint [219,220], so that the Hermiticity of the Hamiltonian is a part of the problem if the mass is not a constant. Nevertheless, different generalized CS have been constructed [249][250][251][252][253][254][255][256][257]. The above is remarkable since well known quantumclassical analogies [38,40,248,[258][259][260] can be exploited to test quantum-theoretical predictions in the laboratory.…”

New Fourier transform containing a pair of complex Euler Γ-functions with a monomial: Mathematical and physical applications

“…In the last decade, there has been great interest to study quantum systems endowed with position-dependent effective mass (PDEM) for Schrödinger equation (see, [12,13,14] and references therein). In our paper [3] we succeeded to construct, analytically and numerically, the Wigner's distribution functions (WDF) for the generalized Laguerre polynomials using to that end an exponentially decaying mass function.…”

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“…Some crucial applications of the coherent states for non-Hermitian system have been studied in various different contexts. They have been applied to the study of meanfield dynamics of Bose-Einstein condensation [178], in the construction of coherent states for time-dependent systems [85], in the study of quantum tomogram [179], in quantum evolution [180], in the study of Fermionic coherent states [181], λ coherent states [182], bicoherent states [184], path integral coherent states [183], complex oscillator systems [185], systems with position dependent mass [186] etc. Moreover, as already discussed that our systems being wellconnected with the nonlinear coherent states, they can be applied to anywhere where the usual nonlinear coherent states are applied.…”