Variational approach to the Schr\"odinger equation with a delta-function potential

• URL: http://arxiv.org/abs/2106.10231v1
• Date: Thu, 17 Jun 2021 13:05:33 GMT
• Title: Variational approach to the Schr\"odinger equation with a delta-function potential
• Authors: Francisco M. Fern\'andez
• Abstract summary: We obtain accurate eigenvalues of the one-dimensional Schr"odinger equation with a Hamiltonian of the form $H_g=H+gdelta (x)$. We show that the well known Rayleigh-Ritz variational method is a suitable approach provided that the basis set account takes into the effect of the Dirac delta on the wavefunction.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We obtain accurate eigenvalues of the one-dimensional Schr\"odinger equation with a Hamiltonian of the form $H_{g}=H+g\delta (x)$, where $\delta (x)$ is the Dirac delta function. We show that the well known Rayleigh-Ritz variational method is a suitable approach provided that the basis set takes into account the effect of the Dirac delta on the wavefunction.

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