Exact Matrix Elements of a Crystal Hamiltonian between Harmonic-Oscillator Wave Functions

1966 ◽  
Vol 144 (2) ◽  
pp. 789-798 ◽  
Author(s):  
T. R. Koehler
Keyword(s):  
Harmonic Oscillator ◽  
Wave Functions ◽  
Matrix Elements ◽  
Exact Matrix

Evaluation of Nuclear Matrix Elements Involving Harmonic Oscillator Wave Functions

1974 ◽  
Vol 52 (4) ◽  
pp. 324-329
Author(s):  
C. K. Scott ◽  
R. N. Singh
Keyword(s):  
Harmonic Oscillator ◽  
Nuclear Matrix ◽  
Wave Functions ◽  
Matrix Elements ◽  
Simplified Form

A simplified form of the integral of products of harmonic oscillator wave functions is presented, with application to the evaluation of common nuclear matrix elements.

AN ALGEBRAIC APPROACH TO A HARMONIC OSCILLATOR PLUS AN INVERSE SQUARE POTENTIAL IN TWO DIMENSIONS

2005 ◽  
Vol 20 (24) ◽  
pp. 5663-5670 ◽  
Author(s):  
SHI-HAI DONG ◽  
GUO-HUA SUN ◽  
M. LOZADA-CASSOU
Keyword(s):  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Algebraic Approach ◽  
Two Dimensions ◽  
Wave Functions ◽  
Matrix Elements ◽  
Ladder Operators ◽  
Radial Wave ◽  
Commutation Relations ◽  
The Matrix

The exact solutions of the Schrödinger equation with a harmonic oscillator plus an inverse square potential are obtained in two dimensions. We construct the ladder operators directly from the radial wave functions and find that these operators satisfy the commutation relations of an SU (1, 1) group. We obtain the explicit expressions of the matrix elements for some related functions ρ and [Formula: see text] with ρ = r2. We also explore another symmetry between the eigenvalues E(r) and E(ir) by substituting r→ir.

scholarly journals IS IT POSSIBLE TO CONSTRUCT THE PROTON STRUCTURE FUNCTION BY LORENTZ-BOOSTING THE STATIC QUARK-MODEL WAVE FUNCTION?

2004 ◽  
Vol 19 (31) ◽  
pp. 5435-5442 ◽  
Author(s):  
Y. S. KIM ◽  
MARILYN E. NOZ
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Structure Function ◽  
Parton Distribution ◽  
Wave Functions ◽  
Proton Structure Function ◽  
Proton Structure ◽  
Static Quark ◽  
Momentum Relation ◽  
Good Agreement

The energy-momentum relations for massive and massless particles are E=p2/2m and E=pc respectively. According to Einstein, these two different expressions come from the same formula [Formula: see text]. Quarks and partons are believed to be the same particles, but they have quite different properties. Are they two different manifestations of the same covariant entity as in the case of Einstein's energy-momentum relation? The answer to this question is YES. It is possible to construct harmonic oscillator wave functions which can be Lorentz-boosted. They describe quarks bound together inside hadrons. When they are boosted to an infinite-momentum frame, these wave functions exhibit all the peculiar properties of Feynman's parton picture. This formalism leads to a parton distribution corresponding to the valence quarks, with a good agreement with the experimentally observed distribution.

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