Application of moment wavelet transform to quantum mechanics, 1998
Ogbazghi, Asmerom Y.
1990-1999
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, 1/ ?,b (p)=??pe-Q\( ?(x +b), where ? -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 1/ ?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) = m?2 + g?4, V(?) = ? 2+?10 respectively.
text
application/pdf
1998-07-01
thesis
Master of Science (MS)
Clark Atlanta University
Physics
Georgia--Atlanta
http://hdl.handle.net/20.500.12322/cau.td:1998_ogbazghi_asmerom_y