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

被引：1

作者：

Chakraborty, Arindam ^{[1
]}

Debnath, Bhaskar ^{[1
]}

Datta, Ritaban ^{[1
]}

Banerjee, Pratyay ^{[2
]}

机构：

[1] Heritage Inst Technol, Dept Phys, Kolkata 700107, India

[2] PR Thakur Govt Coll, Dept Phys, Thakurnagar 743287, India

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2022年 / 32卷 / 05期

关键词：

Spinor; Linearization; Rashba; Inverse square potential; Schrodinger equation; Clifford algebra; Loop algebra; Supersymmetry; DRESSELHAUS; RASHBA;

D O I：

10.1007/s00006-022-01239-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A number of new Levy-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. Moreover the supersymmetric nature of one dimensional harmonic oscillator emerges naturally in this formulation.

引用

页数：13