The scaled Hermite–Weber basis still highly competitive. (English) Zbl 1037.81041

Summary: The effectiveness of the usual harmonic oscillator basis is demonstrated on a wide class of Schrödinger Hamiltonians with various spectral properties. More specifically, it is shown numerically that an appropriately scaled Hermite-Weber basis yields extremely accurate results not only for the energy eigenvalues which differ slightly from the harmonic oscillator levels, but also for the states which reflect a purely anharmonic character.


81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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