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arXiv · 1411.4405

Position-dependent mass Lagrangians: nonlocal transformations, Euler-Lagrange invariance and exact solvability

Omar Mustafa
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Abstract

A general non-local point transformation for position-dependent mass Lagrangians and their mapping into a "constant unit-mass" Lagrangians in the generalized coordinates is introduced. The conditions on the invariance of the related Euler-Lagrange equations are reported. The harmonic oscillator linearization of the PDM Euler-Lagrange equations is discussed through some illustrative examples including harmonic oscillators, shifted harmonic oscillators, a quadratic nonlinear oscillator, and a Morse-type oscillator. The Mathews-Lakshmanan nonlinear oscillators are reproduced and some "shifted" Mathews-Lakshmanan nonlinear oscillators are reported. The mapping of an isotonic nonlinear oscillator into a PDM deformed isotonic oscillator is also discussed.

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Omar Mustafa. 2014-11-17. Position-dependent mass Lagrangians: nonlocal transformations, Euler-Lagrange invariance and exact solvability. https://doi.org/10.1088/1751-8113%2F48%2F22%2F225206

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