A note on the Schrödinger equation for the x2+λx2/(1+g x2) potential
- 1 December 1980
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 21 (12) , 2780-2785
- https://doi.org/10.1063/1.524398
Abstract
The energy levels and wave functions of the Schrödinger equation involving the potential x2+λx2/(1+gx2) are calculated by the variational method, for any range of λ and g, without having to resort to numerical quadrature. Using properly scaled (in λ and g) harmonic oscillator functions as a basis set, an easy to compute analytical expression of the current Hamiltonian matrix element is derived. Perturbative results are also given.Keywords
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