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Register a new userOn the classical and quantum dynamics of a class of nonpolynomial oscillators
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Added by
Chithiika Ruby V Dr
Publication date
2020
fields
Physics
and research's language is
English
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We consider two one dimensional nonlinear oscillators, namely (i) Higgs oscillator and (ii) a $k$-dependent nonpolynomial rational potential, where $k$ is the constant curvature of a Riemannian manifold. Both the systems are of position dependent mass form, ${displaystyle m(x) = frac{1}{(1 + k x^2)^2}}$, belonging to the quadratic Li$acute{e}$nard type nonlinear oscillators. They admit different kinds of motions at the classical level. While solving the quant
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We consider the problem of removal of ordering ambiguity in position dependent mass quantum systems characterized by a generalized position dependent mass Hamiltonian which generalizes a number of Hermitian as well as non-Hermitian ordered forms of the Hamiltonian. We implement point canonical transformation method to map one-dimensional time-independent position dependent mass Schr${o}$dinger equation endowed with potentials onto constant mass counterparts which are considered to be exactly solvable. We observe that a class of mass functions and the corresponding potentials give rise to solutions that do not depend on any particular ordering, leading to the removal of ambiguity in it. In this case, it is imperative that the ordering is Hermitian. For non-Hermitian ordering we show that the class of systems can also be exactly solvable and are also shown to be iso-spectral using suitable similarity transformations. We also discuss the normalization of the eigenfunctions obtained from both Hermitian and non-Hermitian orderings. We illustrate the technique with the quadratic Li${e}$nard type nonlinear oscillators, which admit position dependent mass Hamiltonians.
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