Factorization method and new potentials from the inverted oscillator
arXiv:1206.4519 · doi:10.1016/j.aop.2013.02.015
Abstract
In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in particular, only very specific second-order transformations produce non-singular real potentials. It will be shown that these transformations turn out to be the so-called complex ones. Moreover, we will study the factorization method applied to the inverted oscillator and the algebraic structure of the new Hamiltonians.
19 pages, 8 figures, 2 tables. The new version has a new section for the algebras of the harmonic and inverted oscillators, a new appendix, and color figures
References in corpus (7)
- Infinitely many shape invariant potentials and new orthogonal polynomials
- Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
- Exceptional orthogonal polynomials and the Darboux transformation
- Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
- Inverted Oscillator
- Non-hermitian Hamiltonians and Painlevé IV equation with real parameters
- Coherent states approach to Penning trap
Cited by in corpus (21)
- Theory of strain in single-layer transition metal dichalcogenides
- The Multi-faceted Inverted Harmonic Oscillator: Chaos and Complexity
- Unified Dark Energy and Dust Dark Matter Dual to Quadratic Purely Kinetic K-Essence
- Non-Perturbative Quantum Geometry III
- Trends in supersymmetric quantum mechanics
- On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm
- Wronskian differential formula for k-confluent SUSY QM
- The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
- Recursive Representation of Wronskians in Confluent Supersymmetric Quantum Mechanics
- Stochastic Bohmian mechanics within the Schrödinger-Langevin framework: A trajectory analysis of wave-packet dynamics in a fluctuative-dissipative medium
- Complex oscillator and Painlevé IV equation
- Quantum inverted harmonic potential
- Interactions resolve state-dependence in a toy-model of AdS black holes
- Ladder Operators in Repulsive Harmonic Oscillator with Application to the Schwinger Effect
- Quantum confinement in 1D systems through an imaginary-time evolution method
- Exact solution of the position-dependent mass Schrödinger equation with the completely positive oscillator-shaped quantum well potential
- Quantum Operations: technical or fundamental challenge?
- Non-Hermitian inverted Harmonic Oscillator-Type Hamiltonians Generated from Supersymmetry with Reflections
- Perturbation-based Non-perturbative Method
- Swanson Hamiltonian: non-PT-symmetry phase
- On the diagonalization of quadratic Hamiltonians