The Quantum Mechanics SUSY Algebra: An Introductory Review
R. de Lima Rodrigues
TL;DR
This paper reviews the formulation of N=2 supersymmetry algebra in quantum mechanics starting from classical Lagrangian formalism, applying Dirac quantization, and exploring its applications in nonrelativistic quantum systems.
Contribution
It provides an introductory overview of the SUSY algebra in quantum mechanics derived from classical mechanics using Dirac quantization, highlighting its structure and applications.
Findings
N=2 supersymmetry algebra is constructed in quantum mechanics.
Eigenfunctions are analyzed within the Schrödinger picture.
Applications of SUSY algebra in quantum systems are discussed.
Abstract
Starting with the Lagrangian formalism with N=2 supersymmetry in terms of two Grassmann variables in Classical Mechanics, the Dirac canonical quantization method is implemented. The N=2 supersymmetry algebra is associated to one-component and two-component eigenfunctions considered in the Schr\"odinger picture of Nonrelativistic Quantum Mechanics. Applications are contemplated.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Quantum chaos and dynamical systems · Nonlinear Photonic Systems