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Construction of a Few Quantum Mechanical Hamiltonians via Lévy-Leblond Type Linearization: Clifford Momentum, Spinor States and Supersymmetry

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Abstract

A number of new Lévy-Leblond type equations admitting four component spinor solutions have been proposed. The pair of linearized equations thus obtained in each case lead to Hamiltonians with characteristic features like L-S coupling and supersymmetry. The relevant momentum operators have often been understood in terms of Clifford algebraic bases producing Schrödinger Hamiltonians with L-S coupling. As for example, Hamiltonians representing Rashba effect or three dimensional harmonic oscillator have been constructed. Moreover the supersymmetric nature of one dimensional harmonic oscillator emerges naturally in this formulation.

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Acknowledgements

A.C. wishes to thank his colleague Dr. Baisakhi Mal for her valuable assistance in preparing the latex version.

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Authors and Affiliations

  1. Department of Physics, Heritage Institute of Technology, Kolkata, 700107, India

    Arindam Chakraborty, Bhaskar Debnath & Ritaban Datta

  2. Department of Physics, P. R. Thakur Govt. College, Thakurnagar, 743287, India

    Pratyay Banerjee

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  1. Arindam Chakraborty
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Correspondence to Arindam Chakraborty.

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Chakraborty, A., Debnath, B., Datta, R. et al. Construction of a Few Quantum Mechanical Hamiltonians via Lévy-Leblond Type Linearization: Clifford Momentum, Spinor States and Supersymmetry. Adv. Appl. Clifford Algebras 32, 56 (2022). https://doi.org/10.1007/s00006-022-01239-7

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  • DOI: https://doi.org/10.1007/s00006-022-01239-7

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