POTENTIAL REPRESENTATION METHOD FOR THE SCHRÖDINGER EQUATION
| Autor: | Donatas Jurgaitis, A.J. Janavičius, Sigita Turskienė |
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| Rok vydání: | 2011 |
| Předmět: |
Partial differential equation
Discretization Mathematical analysis Green’s function Electric-field integral equation Summation equation Variation of parameters Integral equation Schrodinger equation Schrödinger equation symbols.namesake integral equation iterative method boundary value problem Modeling and Simulation QA1-939 symbols Mathematics Analysis Harmonic oscillator |
| Zdroj: | Mathematical Modelling and Analysis; Vol 16 No 3 (2011); 442-450 Mathematical Modelling and Analysis, Vol 16, Iss 3 (2011) |
| ISSN: | 1648-3510 1392-6292 |
| 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: | OpenAIRE |
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