A new iterative method for solving the time-independent Schrödinger equation based on the generalized Bloch equation. I. Boson systems: The quartic anharmonic oscillator
✍ Scribed by Holger Meiβner; E. Otto Steinborn
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 251 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0020-7608
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✦ Synopsis
The eigenvalue problem of the time-independent Schrodinger equation is solved as usual by expanding the eigenfunctions in terms of a basis set. However, the wave-function Ž . expansion coefficients WECs , which are certain matrix elements of the wave operator, are determined by an iterative method. For these WECs, we deduced new nonlinear equations utilizing the concept of a reference space and the generalized Bloch equation for the wave operator. To test these equations, the method is used to calculate with great accuracy the energy eigenvalues of the ground state and first few excited states of the quartic anharmonic oscillator, whose Rayleigh᎐Schrodinger perturbation series diverges strongly for every nonzero coupling constant.