# The variational method applied to the harmonic oscillator in the presence of a delta function potential

@article{Ghose2021TheVM, title={The variational method applied to the harmonic oscillator in the presence of a delta function potential}, author={Indrajit Ghose and Parongama Sen}, journal={European Journal of Physics}, year={2021}, volume={42} }

The problem of the harmonic oscillator with a centrally located delta function potential can be exactly solved in one dimension, where the eigenfunctions are expressed as superpositions of the Hermite polynomials or as confluent hypergeometric functions in general. The eigenfunctions obtained exactly are difficult to visualise and hence, to gain more insight, one can attempt to use model wave functions which are explicitly and simply expressed. Here, we apply the variational method to verify…

## 2 Citations

### Analytical study of the sth-order perturbative corrections to the solution to a one-dimensional harmonic oscillator perturbed by a spatially power-law potential Vper(x) = λxα

- Mathematics, PhysicsAIP Advances
- 2021

In this work, we present a rigorous mathematical scheme for the derivation of the sth-order perturbative corrections to the solution to a one-dimensional harmonic oscillator perturbed by the…

### Variational approach to the Schrödinger equation with a delta-function potential

- Mathematics, PhysicsEuropean Journal of Physics
- 2021

We obtain accurate eigenvalues of the one-dimensional Schrödinger equation with a Hamiltonian of the form H g = H + gδ(x), where δ(x) is the Dirac delta function. We show that the well known…

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