Rational Extension of Quantum Anisotropic Oscillator Potentials with Linear and/or Quadratic Perturbations

2025/04/11 by Rajesh Kumar Yadav, Rajesh Kumar, Yadav, Rajesh Kumar +3
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum and Classical Electrodynamics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2504.08236

openalex publication_date 2025/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a comprehensive study of the rational extension of the quantum anisotropic harmonic oscillator (QAHO) potentials with linear and/or quadratic perturbations. For the one-dimensional harmonic oscillator plus imaginary linear perturbation (iλx), we show that the rational extension is possible not only for the even but also for the odd co-dimensions m. In two-dimensional case, we construct the rational extensions for QAHO potentials with quadratic (λ xy) perturbation both when λ is real or imaginary and obtain their solutions. Finally, we extend the discussion to the three-dimensional QAHO with linear and quadratic perturbations and obtain the corresponding rationally extended potentials. For all these cases, we obtain the conditions under which the spectrum remains real and also when there is degeneracy in the system.

Citations

• Rational Extension of Anisotropic Harmonic Oscillator Potentials in Higher Dimensions
• A Class of Exactly Solvable Real and Complex PT Symmetric Reflectionless Potentials
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• The Scattering amplitude for Newly found exactly solvable Potential
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• Solvable rational extensions of the isotonic oscillator
• Another set of infinitely many exceptional (Xℓ) Laguerre polynomials
• Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomials
• Infinitely many shape invariant potentials and new orthogonal polynomials
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
• An Extension of Bochner's Problem: Exceptional Invariant Subspaces
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Real Spectra in Non-Hermitian Hamiltonians HavingPTSymmetry

Related

• Rational Extension of Anisotropic Harmonic Oscillator Potentials in Higher Dimensions
• Equivalent non-rational extensions of the harmonic oscillator, their ladder operators and coherent states
• Quantum oscillator of quartic anharmonicity
• Parameter space geometry of the quartic oscillator and the double well potential: Classical and quantum description
• Multi-point quasi-rational approximants for the energy eigenvalues of potentials of the form V(x)= Ax^a + Bx^b