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• W3100105436 abstract "A complete variational treatment is provided for a family of spiked-harmonic oscillator Hamiltonians H = -d^2/dx^2 + B x^2 + lambda/x^alpha, B > 0, lambda > 0, for arbitrary alpha > 0. A compact topological proof is presented that the set S = {psi_n} of known exact solutions for alpha = 2 constitutes an orthonormal basis for the Hilbert space L_2(0, infinity). Closed-form expressions are derived for the matrix elements of H with respect to S. These analytical results, and the inclusion of a further free parameter, facilitate optimized variational estimation of the eigenvalues of H to high accuracy." @default.
• W3100105436 created "2020-11-23" @default.
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• W3100105436 date "2002-01-01" @default.
• W3100105436 modified "2023-10-18" @default.
• W3100105436 title "Spiked harmonic oscillators" @default.
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• W3100105436 doi "https://doi.org/10.1063/1.1418247" @default.
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