Construction of a few Quantum mechanical Hamiltonians via L\acuteevi-Leblond type Linearization:Spinor states and Supersymmetry

2019/03/07 by Arindam Chakraborty, Chakraborty, Arindam, Bhaskar Debnath +5
Physics and Astronomy · Mathematics · #Quantum Mechanics and Non-Hermitian Physics #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1903.02734

Abstract

A number of new L\acuteevi-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 Schrodinger Hamiltonians with L-S coupling. As for example Hamiltonians representing Rashba effect or three dimensional harmonic oscillator have been constructed. The supersymmetric nature of one dimensional oscillator has also been appreciated.

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