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

被引：0
作者：
Arindam Chakraborty
Bhaskar Debnath
Ritaban Datta
Pratyay Banerjee
机构：
[1] Heritage Institute of Technology,Department of Physics
[2] P. R. Thakur Govt. College,Department of Physics
来源：
Advances in Applied Clifford Algebras | 2022年 / 32卷
关键词：
Spinor; Linearization; Rashba; Inverse square potential; Schrödinger equation; Clifford algebra; Loop algebra; Supersymmetry; 81R25;
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摘要：
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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