Abstract
The Hill-series method is shown to have several advantages for treating the Schrödinger equation when the wavefunction obeys the Dirichlet boundary condition Ψ(R) = 0. A novel combination of the virial theorem, the Hill-series method and a finite difference method is used to find the node positions of the wavefunction for several excited states of perturbed oscillator and coulombic systems and to find critical radii for the hydrogen atom.
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