Nonstationary deformed singular oscillator: quantum invariants and the factorization method
arXiv:2001.06764 · doi:10.1088/1742-6596/1540/1/012017
Abstract
New families of time-dependent potentials related with the stationary singular oscillator are introduced. This is achieved after noticing that a non stationary quantum invariant can be constructed for the singular oscillator. Such invariant depends on coefficients that are related to solutions of an Ermakov equation, the latter becomes essential since it guarantees the regularity of the solutions at each time. In this form, after applying the factorization method to the quantum invariant, rather than the Hamiltonian, one manages to introduce the time parameter into the transformation, leading to factorized operators which are the constants of motion of the new time-dependent potentials. Under the appropriate limit, the initial quantum invariant reduces to the stationary singular oscillator Hamiltonian, in such case, one recovers the families of potentials obtained through the conventional factorization method and previously reported in the literature. In addition, some special limits are discussed such that the singular barrier of the potential vanishes, leading to non-singular time-dependent potentials.
References in corpus (22)
- Supersymmetry without hermiticity
- First-order intertwining operators and position-dependent mass Schrodinger equations in d dimensions
- New Shape Invariant Potentials in Supersymmetric Quantum Mechanics
- The finite difference algorithm for higher order supersymmetry
- Position Dependent Mass Oscillators and Coherent States
- Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics
- Riccati equation, Factorization Method and Shape Invariance
- -symmetric invisible defects and confluent Darboux-Crum transformations
- New supersymmetry-generated complex potentials with real spectra
- New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials
- Bi-Orthogonal Approach to Non-Hermitian Hamiltonians with the Oscillator Spectrum: Generalized Coherent States for Nonlinear Algebras
- Rationally-extended radial oscillators and Laguerre exceptional orthogonal polynomials in kth-order SUSYQM
- Intertwining relations of non-stationary Schrödinger operators
- Quantum singular oscillator as a model of two-ion trap: an amplification of transition probabilities due to small time variations of the binding potential
- Photonic systems with two-dimensional landscapes of complex refractive index via time-dependent supersymmetry
- Interplay between Riccati, Ermakov and Schroedinger equations to produce complex-valued potentials with real energy spectrum
- SU(1,1) Coherent States For Position-Dependent Mass Singular Oscillators
- Quantum nonstationary oscillators: Invariants, dynamical algebras and coherent states via point transformations
- Coherent states for exactly solvable time-dependent oscillators generated by Darboux transformations
- Supersymmetric partners of the harmonic oscillator with an infinite potential barrier
- Coherent states for the supersymmetric partners of the truncated oscillator
- Time-dependent rational extensions of the parametric oscillator: quantum invariants and the factorization method