Exact solution and coherent states of an asymmetric oscillator with position-dependent mass

Abstract

We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. {\bf 62}, 092101 (2021)] in the classical and quantum formalisms, by introducing the effect of the mass function in both kinetic and potential energies. The resulting Hamiltonian is mapped into a Morse oscillator by means of a point canonical transformation from the usual phase space $(x,p)$ to a deformed one $(x_{\gamma },{\Pi }_{\gamma })$. Similar to the Morse potential, the deformed oscillator presents bound trajectories in phase space corresponding to an anharmonic oscillatory motion in classical formalism and, therefore, bound states with a discrete spectrum in quantum formalism. On the other hand, open trajectories in phase space are associated with scattering states and continuous energy spectrum. Employing the factorization method, we investigate the properties of the coherent states, such as the time evolution and their uncertainties. A fast localization, classical and quantum, is reported for the coherent states due to the asymmetrical position-dependent mass. An oscillation of the time evolution of the uncertainty relationship is also observed, whose amplitude increases as the deformation increases.

arXiv comment24 pages, 11 figures

References in corpus (24)

• Effective Mass of One 4he Atom in Liquid 3he
• Experimental nonclassicality of single-photon-added thermal light states
• Displacement operator for quantum systems with position-dependent mass
• Ordering ambiguity revisited via position dependent mass pseudo-momentum operators
• A Quantum Exactly Solvable Nonlinear Oscillator with quasi-Harmonic Behaviour
• Morse potential derived from first principles
• Amplification of realistic cat-like states by homodyne heralding
• A position-dependent mass harmonic oscillator and deformed space
• Classification of Lie point symmetries for quadratic Li$\acute{\text{e}}$nard type equation $\ddot{x}+f(x){\dot{x}}^2+g(x)=0$
• PDM creation and annihilation operators of the harmonic oscillators and the emergence of an alternative PDM-Hamiltonian
• Generalized space and linear momentum operators in quantum mechanics
• Position-dependent mass, finite-gap systems, and supersymmetry
• $\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass
• Effective-Mass Dirac Equation for Woods-Saxon Potential: Scattering, Bound States and Resonances
• Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator
• Algebraic solutions of shape-invariant position-dependent effective mass systems
• Energy eigenfunctions for position-dependent mass particles in a new class of molecular hamiltonians
• Conformal bridge between asymptotic freedom and confinement
• Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators
• Generalized semiconfined harmonic oscillator model with a position-dependent effective mas
• Supersymmetric quantum mechanics and coherent states for a deformed oscillator with position-dependent effective mass
• Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis
• Generalized coherent states for position-dependent effective mass systems
• Construction of coherent states for Morse potential: A su(2)-like approach

Cited by in corpus (2)

• The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass
• On the $\mathcal{P}\mathcal{T}$-symmetric parametric amplifier