Supersymmetry in quantum mechanics

Journal Article · Fri Apr 20 04:00:00 EDT 1990 · International Journal of Modern Physics A; (USA)

DOI:https://doi.org/10.1142/S0217751X90000647· OSTI ID:6135925

Lahiri, A ^[1]; Roy, P K ^[2]; Bagghi, B ^[3]

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1. Dept. of Theoretical Physics, Indian Association for the Cultivation of Science, Calcutta 700032 (IN)
2. Dept. of Physics, Barasat Government College, Barasat 743201, West Bengal (IN)
3. Dept. of Applied Mathematics, Vidyasagar Univ., Midnapore 721102, West Bengal (IN)

A pedagogical review on supersymmetry in quantum mechanics is presented which provides a comprehensive coverage of the subject. First, the key ingredients of the quantization of the systems with anticommuting variables are discussed. The supersymmetric Hamiltonian in quantum mechanics is then constructed by emphasizing the role of partner potentials and the superpotentials. The authors also make explicit the mathematical formulation of the Hamiltonian by considering in detail the N = 1 and N = 2 supersymmetric (quantum) mechanics. Supersymmetry is then discussed in the context of one-dimensional problems and the importance of the factorization method is highlighted. They treat in detail the technique of constructing a hierarchy of Hamiltonians employing the so-called 'shape-invariance' of potentials. To make transparent the relationship between supersymmetry and solvable potentials, they also solve several examples. They then go over the formulation of supersymmetry in radial problems, paying a special attention to the Coulomb and isotropic oscillator potentials. They show that the ladder operator technique may be suitable modified in higher dimensions for generating isospectral Hamiltonians. Next, the criteria for the breaking of supersymmetry is considered and their range of applicability is examined by suitably modifying he definition of Witten's index. Finally, the authors perform some numerical calculations for a class of potentials to show how a modified WKB approximation works in supersymmetric cases.

• OSTI ID: 6135925
• Journal Information: International Journal of Modern Physics A; (USA), Journal Name: International Journal of Modern Physics A; (USA) Vol. 5:8; ISSN IMPAE; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

645300* -- High Energy Physics-- Particle Invariance Principles & Symmetries
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CALCULATION METHODS
FACTORIZATION
HAMILTONIANS
MATHEMATICAL OPERATORS
MECHANICS
NUMERICAL SOLUTION
QUANTUM MECHANICS
QUANTUM OPERATORS
SUPERSYMMETRY
SYMMETRY
SYMMETRY BREAKING
WKB APPROXIMATION