Perturbation theory in a framework of iteration methods

Abstract

In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the `asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this paper, we study perturbed problems in quantum mechanics and we use the method to find the coefficients in the perturbation series for the eigenvalues and eigenfunctions directly, without first solving the unperturbed problem.

13 pages

References in corpus (20)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• PT-Symmetric Quantum Mechanics
• Asymptotic iteration method for eigenvalue problems
• Construction of exact solutions to eigenvalue problems by the asymptotic iteration method
• Variational perturbation expansion for strong-coupling coefficients of the anharmonic oscillator
• A family of complex potentials with real spectrum
• PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model
• Convergence of Scaled Delta Expansion: Anharmonic Oscillator
• Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant
• Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics
• Multiple-Scale Analysis of the Quantum Anharmonic Oscillator
• Theory and Computation of the Spheroidal Wave Functions
• Model of supersymmetric quantum field theory with broken parity symmetry
• PT symmetric pseudo-perturbation recipe; an imaginary cubic oscillator with spikes
• Non-Hermitian matrix description of the PT symmetric anharmonic oscillators
• Optimized Perturbation Theory for Wave Functions of Quantum Systems
• A new method for the solution of the Schrodinger equation
• Comparative study of quantum anharmonic potentials
• Anharmonic oscillators energies via artificial perturbation method
• Solvable analogue of the imaginary cubic oscillator

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• Closed analytical solutions of the d-dimensional Schrödinger equation with deformed Woods-Saxon potential plus double ring-shaped potential
• Parameterized quasinormal frequencies and Hawking radiation for axial gravitational perturbations of a holonomy-corrected black hole
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