scholarly journals Momentum representation of Coulomb wave functions and level shifts in bottomonium due to charm effects

2004 ◽  
Vol 70 (9) ◽  
Author(s):  
Haibin Wang ◽  
York-Peng Yao
Keyword(s):  
Wave Functions ◽  
Momentum Representation ◽  
Level Shifts

scholarly journals Alternating Coordinate-Momentum Representation for Quantum States Based on Bopp Operators for Modelling Long-Distance Coherence Aspects

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ezzat G. Bakhoum ◽  
Cristian Toma
Keyword(s):  
Wave Train ◽  
Linear Equations ◽  
Quantum States ◽  
Wave Functions ◽  
Momentum Representation ◽  
Long Distance ◽  
Support Functions ◽  
Vector Potentials ◽  
Time Origin ◽  
Good Manner

This study presents an alternating coordinate-momentum representation for propagation and transition of associated wave function, based on Bopp operators and on a certain symbolic determinant corresponding to a set of two linear equations with null free terms. It is shown that this alternating representation can justify in a good manner the patterns created through reflection/refraction of waves on nonperfectly smooth interfaces and phase correspondence of diffracted beams without the need of supplementary support functions. Correlations with Lorentz transformation of wave functions by interaction with a certain material medium (the space-time origin of a wave-train being adjusted) are also presented, and supplementary aspects regarding the use of electromagnetic scalar and vector potentials for modelling evolution within this alternating representation are added.

Transition from discrete to continuous spectrum: separable potential in one dimension

1990 ◽  
Vol 68 (4-5) ◽  
pp. 394-402 ◽  
Author(s):  
J. G. Muga ◽  
R. F. Snider
Keyword(s):  
Perturbation Theory ◽  
Phase Shift ◽  
Continuous Spectrum ◽  
Wave Functions ◽  
Phase Factor ◽  
One Dimension ◽  
Separable Potential ◽  
Level Shift ◽  
Momentum Representation ◽  
Convergence Parameter

An analysis is made of the transition from the discrete to the continuous spectrum for a separable potential in one dimension. The role played by the length of the box and the convergence parameter, ε, in the different limiting operations is discussed. Relations are found between scattering and perturbation theory matrices and wave functions in momentum representation. In particular, the known expression relating the level shift to the phase shift is recovered. The scattering and Brillouin–Wigner perturbation wave functions are in general not simply related by a phase factor.

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