New Solvable Singular Potentials
arXiv:hep-th/0011096 · doi:10.1088/0305-4470/34/19/311
Abstract
We obtain three new solvable, real, shape invariant potentials starting from the harmonic oscillator, Pöschl-Teller I and Pöschl-Teller II potentials on the half-axis and extending their domain to the full line, while taking special care to regularize the inverse square singularity at the origin. The regularization procedure gives rise to a delta-function behavior at the origin. Our new systems possess underlying non-linear potential algebras, which can also be used to determine their spectra analytically.
19 pages, 4 figures
References in corpus (15)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Supersymmetry and Quantum Mechanics
- PT-Symmetric Quantum Mechanics
- Schrödinger operators with complex potential but real spectrum
- PT -symmetric harmonic oscillators
- SUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra
- sl(2, C) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues
- Algebraic Approach to Shape Invariance
- New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity
- Exact solution for Morse oscillator in PT-symmetric quantum mechanics
- Algebraic Shape Invariant Models
- Potentials with Two Shifted Sets of Equally Spaced Eigenvalues and Their Calogero Spectrum
- Harmonic oscillator well with a screened Coulombic core is quasi-exactly solvable
- Is the Lowest Order Supersymmetric WKB Approximation Exact for All Shape Invariant Potentials ?
- Coordinate Realizations of Deformed Lie Algebras with Three Generators
Cited by in corpus (8)
- A quantum exactly solvable non-linear oscillator related with the isotonic oscillator
- Non-Hermitian supersymmetry and singular PT symmetrized oscillators
- Relativistic and nonrelativistic bound states of the isotonic oscillator by Nikiforov-Uvarov method
- SUSY Intertwining Relations of Third Order in Derivatives
- Superintegrable quantum u(3)--systems and higher rank factorizations
- Comment on "Supersymmetry and Singular Potentials" by Das and Pernice [Nucl. Phys. B 561 (1999) 357]
- Algebraic Shape Invariant Potentials as the Generalized Deformed Oscillator
- Dynamical symmetries for superintegrable quantum systems