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