Analytical treatment of the Yukawa potential

Abstract

Using a suitable Laguerre basis set that ensures a tridiagonal matrix representation of the reference Hamiltonian, we were able to evaluate exactly the matrix elements of the Yukawa potential in this representation. This enabled us to compute the bound state spectrum as the eigenvalues of the associated analytical matrix representing the full Hamiltonian. We also used the complex scaling method to evaluate the resonance energies and compared our results with those obtained using the Gauss quadrature approach and the corresponding results from the literature.