Periodic Potentials and Supersymmetry
arXiv:quant-ph/0402206 · doi:10.1088/0305-4470/37/43/002
Abstract
We review the current status of one dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics, one can considerably enlarge the limited class of analytically solvable one-dimensional periodic potentials. Further, using the Landen transformations as well as cyclic identities for Jacobi elliptic functions discovered by us recently, it is shown that a linear superposition of Lamé (as well as associated Lamé) potentials are also analytically solvable. Finally, using anti-isospectral transformations, we also obtain a class of analytically solvable, complex, PT-invariant, periodic potentials having real band spectra.
27 pages, 4 figures
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Cited by in corpus (14)
- Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
- Finite-gap systems, tri-supersymmetry and self-isospectrality
- New supersymmetry-generated complex potentials with real spectra
- Trends in supersymmetric quantum mechanics
- Supersymmetry-guided method for mode selection and optimization in coupled systems
- New supersymmetric partners for the associated Lame potentials
- Complex Periodic Potentials with a Finite Number of Band Gaps
- PT-Invariant Periodic Potentials with a Finite Number of Band Gaps
- Supersymmetric Biorthogonal Quantum Systems
- Conditional quasi-exact solvability of the quantum planar pendulum and of its anti-isospectral hyperbolic counterpart
- Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
- Dirac equation with complex potentials
- Second-order topology and supersymmetry in two-dimensional topological insulators
- Bilayer graphene in periodic and quasiperiodic magnetic superlattices