In this work we reconstruct Quantum Mechanical wave functions for some confining potentials, using the moment-wavelet method of Handy and Murenzi. This method consists in transforming the Schrodinger equation into an equivalent continuous wavelet transform (CWT) representation involving scaled and translated moments, µ1/ α,b (p)=∫χpe-Q\( Ψ(x +b), where ϐ -Q becomes the mother wavelet. The discrete bound states are determined through a multiscale process involving the integration of a finite number of coupled linear first order differential equation in the moments µ1/ α,b (p). The underlying initial value problem depends on moment quantization methods to determine the infinite scale (a = ∞) moments and energy. Using this method we calculate the energies and wavefunctions for the first two quantum states of quartic and dectic anharmonic oscillator potentials, V(x) = mχ2 + gχ4, V(χ) = χ 2+χ10 respectively.
| Identifer | oai:union.ndltd.org:auctr.edu/oai:digitalcommons.auctr.edu:dissertations-4835 |
| Date | 01 July 1998 |
| Creators | Ogbazghi, Asmerom Y. |
| Publisher | DigitalCommons@Robert W. Woodruff Library, Atlanta University Center |
| Source Sets | Atlanta University Center |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | ETD Collection for AUC Robert W. Woodruff Library |
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