Dynamic-group approach to the x2+λx2/(1+g x2) potential

DOI10.1063/1.527140zbMath0603.22007OpenAlexW2089935721MaRDI QIDQ3739370

Guido Vanden Berghe, H. E. De Meyer, Veerle Fack

Publication date: 1986

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.527140

zbMATH Keywords

time-independent Schrödinger equationalgebraic solutiondynamical Lie algebra

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70)

Related Items (11)

Numerical methods for the eigenvalue determination of second-order ordinary differential equations ⋮ A finite-difference method for the numerical solution of the Schrödinger equation ⋮ An extended Numerov-type method for the numerical solution of the Schrödinger equation ⋮ A generator of high-order embedded \(P\)-stable methods for the numerical solution of the Schrödinger equation ⋮ Double exponential sinc-collocation method for solving the energy eigenvalues of harmonic oscillators perturbed by a rational function ⋮ Exact solution of the relativistic finite-difference equation for the Coulomb plus a ring-shaped-like potential ⋮ Exact solutions for nonpolynomial potentials in N-space dimensions using a factorization method and supersymmetry ⋮ Lower bounds for quartic anharmonic and double-well potentials ⋮ A new finite difference scheme with minimal phase-lag for the numerical solution of the Schrödinger equation. ⋮ Approximate solutions to the Klein-Fock-Gordon equation for the sum of Coulomb and ring-shaped-like potentials ⋮ An accurate finite difference method for the numerical solution of the Schrödinger equation

Cites Work

• A finite difference approach for the calculation of perturbed oscillator energies
• A simple iterative solution of the Schrodinger equation in matrix representation form
• On the interaction of the type λx2/(1+g x2)
• On the x²+λx²/(1+gx²) interaction
• Exact solutions of the Schrodinger equation (-d/dx²+x²+ λx²/(1 +gx²))ψ(x) =Eψ(x)

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