Potential representation method for the Schrödinger equation
| Autor: | Arvydas Juozapas Janavičius, Donatas Jurgaitis, Sigita Turskienė |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Mathematical Modelling and Analysis, Vol 16, Iss 3 (2011) |
| Druh dokumentu: | article |
| ISSN: | 13926292 1392-6292 1648-3510 |
| DOI: | 10.3846/13926292.2011.602987 |
| Popis: | A general solution of the Schrödinger equation in the potential representation has been obtained in the form of integral equations. In this representation, the wave function for positive and negative energies or bound states can be expressed as a product of the unperturbed solution for model potential and the function which depends on the additional potential or potential perturbation. Here we have proved that this method is equivalent to the method of variation of constants for negative energies. The linearly independent solutions of Schrödinger equation for harmonic oscillator potential have been obtained for derivation of integral equations, which are used for finding eigenfunctions and eigenvalues for Woods–Saxon potential. Eigenvalues obtained by numerical iterations of these integral equations are in good agreement with results obtained by the discretization method. The kernels of the obtained integral equations are proportional to the perturbation or difference of Woods–Saxon and harmonic oscillator potentials. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|