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 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 onedimensional and a set of n-dimensional PDM-DHO illustrative examples are reported along with their phase-space trajectories.