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arXiv · 2107.14617

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

Omar Mustafa
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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.

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Omar Mustafa. 2021-07-29. $n$-dimensional PDM-damped harmonic oscillators: Linearizability, and exact solvability. https://doi.org/10.1088/1402-4896%2Fabf06a

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