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

Taşeli, H.; Erseçen, M. Bahar

J. Math. Chem. 34, No. 3-4, 177-187 (2003).

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.

MSC:

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

Keywords:

Schrödinger equation; quantum mechanical oscillators; orthogonal expansions; Hermite-Weber functions