On quantized Liénard oscillator and momentum dependent mass
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In this paper, the analytical structure of the nonlinear Lienard oscillator was examined and it was shown that it is a bi-Hamiltonian system depending upon the choice of the coupling parameters.Abstract:
We examine the analytical structure of the nonlinear Lienard oscillator and show that it is a bi-Hamiltonian system depending upon the choice of the coupling parameters. While one has been recently studied in the context of a quantized momentum-dependent mass system, the other Hamiltonian also reflects a similar feature in the mass function and also depicts an isotonic character. We solve for such a Hamiltonian and give the complete solution in terms of a confluent hypergeometric function.read more
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Nonstandard Hamiltonian structures of the Liénard equation and contact geometry
TL;DR: In this paper, the construction of nonstandard Lagrangians and Hamiltonian structures for Lienard equations satisfying Chiellini condition is presented and their connection to time-dependent Hamiltonian formalism is discussed.
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Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations
TL;DR: The present work is intended to be complementary to other papers of the same nature and subject in current circulation to clarify concepts and notions, including some passages of the history of science, with the aim of facilitating the subject for nonspecialists.
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$\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass
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κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass
TL;DR: In this paper, a particle with a position-dependent mass in the context of a deformed algebraic structure (called κ-algebra), motivated by the Kappa-statistics, is presented.
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Exploring branched Hamiltonians for a class of nonlinear systems
TL;DR: In this paper, the authors explore certain classes of branched Hamiltonians in the context of nonlinear autonomous differential equation of Lienard type and two eligible elementary nonlinear models that emerge are shown to admit a feasible quantization along these lines.
References
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Structure and energetics of mixed 4 He- 3 He drops
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A search for shape-invariant solvable potentials
TL;DR: In this paper, a simple method of constructing potentials which is related to the work of Bhattacharjie and Sudarshan (1962) and for which the Schrodinger equation can be solved in terms of known special functions was investigated.