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| Titel: |
On the quantization of the potential amplitude in the Schrödinger equation |
| Auteur: |
Balagurov, B.Ya. |
| Verschenen in: |
Journal of computational methods in sciences and engineering |
| Paginering: | Jaargang 10 (2011) nr. 3-6 pagina's 105-127 |
| Jaar: |
2011-02-25 |
| Inhoud: |
A consistent scheme is proposed for quantizing the potential amplitude in the Schrödinger equation in the case of negative energies (lying in the discrete-spectrum domain). The properties of the eigenfunctions φ_{ν}(r) and eigenvalues α_{ν} corresponding to zero, small, and large absolute values of energy E < 0 are analyzed. Expansion in the set φ_{ν}(r) is used to develop a regular perturbation theory (for E < 0), and a general expression is found for the Green function associated with the time-independent Schrödinger equation. A similar method is used to solve several physical problems: the polarizability of a bound quantum-mechanical system, the two-center problem, and the elastic scattering of slow particles. The proposed approach is advantageous in that it does not require the use of continuum states (for E > 0). |
| Uitgever: |
IOS Press |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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