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

2021/06/17 by Francisco M. Fernández, Fernández, Francisco M.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.2106.10231

arxiv created 2021/06/17 · arxiv updated 2021/06/21

Abstract

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 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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