$n$-dimensional PDM-damped harmonic oscillators: Linearizability, and exact solvability

Abstract

We consider position-dependent mass (PDM) Lagrangians/Hamiltonians in their standard textbook form, where the long-standing \emph{gain-loss balance} between the kinetic and potential energies is kept intact to allow conservation of total energy (i.e., $L=T-V$, $H=T+V$, and $dH/dt=dE/dt=0$). Under such standard settings, we discuss and report on $n$-dimensional PDM damped harmonic oscillators (DHO). We use some $n$-dimensional point canonical transformation to facilitate the linearizability of their $n$-PDM dynamical equations into some $n$-linear DHOs' dynamical equations for constant mass setting. Consequently, the well know exact solutions for the linear DHOs are mapped, with ease, onto the exact solutions for PDM DHOs. A set of one-dimensional and a set of $n$-dimensional PDM-DHO illustrative examples are reported along with their phase-space trajectories.

15 pages, 20 figures

References in corpus (15)

• Ordering ambiguity revisited via position dependent mass pseudo-momentum operators
• Quantum particles trapped in a position-dependent mass barrier; a d-dimensional recipe
• Reduction of superintegrable systems: the anisotropic harmonic oscillator
• Position Dependent Mass Oscillators and Coherent States
• Position-dependent mass Lagrangians: nonlocal transformations, Euler-Lagrange invariance and exact solvability
• Generalized nonlinear oscillators with quasi-harmonic behaviour: classical solutions
• $\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass
• $\eta$-weak-Pseudo-Hermiticity generators and exact solvability
• Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass
• Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
• On the complete integrability of a nonlinear oscillator from group theoretical perspective
• Quantization of Hamiltonian systems with a position dependent mass: Killing vector fields and Noether momenta approach
• Comment on 'Two-dimensional position-dependent massive particles in the presence of magnetic fields"
• Classical oscillator with position-dependent mass in a complex domain
• A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog

Cited by in corpus (1)

• A Class of Isochronous and Non-Isochronous Nonlinear Oscillators