Supersymmetric Quantum Mechanics

Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulae concerning SUSY QM of first second order for one-dimensional arbitrary systems, we will...

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Bibliographic Details
Published inAIP conference proceedings Vol. 1287; no. 1
Main Authors David, J., Fernandez, C.
Format Journal Article
LanguageEnglish
Published United States 11.10.2010
Subjects
ALGEBRA
ANNIHILATION OPERATORS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EIGENSTATES
ELECTROMAGNETIC RADIATION
ENERGY GAP
EQUATIONS
FUNCTIONAL ANALYSIS
HAMILTONIANS
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PERIODICITY
POTENTIALS
QUANTUM MECHANICS
QUANTUM OPERATORS
RADIATIONS
SCHROEDINGER EQUATION
SUPERSYMMETRY
SYMMETRY
VARIATIONS
VISIBLE RADIATION
WAVE EQUATIONS
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Summary:Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulae concerning SUSY QM of first second order for one-dimensional arbitrary systems, we will illustrate the method through the trigonometric Poeschl-Teller potentials. Some intrinsically related subjects, as the algebraic structure inherited by the new Hamiltonians and the corresponding coherent states will be analyzed. The technique will be as well implemented for periodic potentials, for which the corresponding spectrum is composed of allowed bands separated by energy gaps.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.3507423