Methods of establishing the asymptotic behavior of the harmonic oscillator wave functions

1980 ◽  
Vol 48 (4) ◽  
pp. 307-307 ◽  
Author(s):  
Marshall Bowen ◽  
Joseph Coster
Keyword(s):  
Asymptotic Behavior ◽  
Harmonic Oscillator ◽  
Wave Functions

Exact wave functions of a harmonic oscillator with time-dependent mass and frequency

1997 ◽  
Vol 55 (4) ◽  
pp. 3219-3221 ◽  
Author(s):  
I. A. Pedrosa
Keyword(s):  
Harmonic Oscillator ◽  
Wave Functions ◽  
Time Dependent ◽  
Dependent Mass

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.

ENERGY-DEPENDENT POTENTIAL AND NORMALIZATION OF WAVE FUNCTION

2013 ◽  
Vol 28 (18) ◽  
pp. 1350079 ◽  
Author(s):  
A. BENCHIKHA ◽  
L. CHETOUANI
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Spectral Decomposition ◽  
Wave Functions ◽  
Integral Approach ◽  
Path Integral Approach ◽  
Dependent Potential ◽  
Energy Dependent

The problem of normalization related to energy-dependent potentials is examined in the context of the path integral approach, and a justification is given. As examples, the harmonic oscillator and the hydrogen atom (radial) where, respectively the frequency and the Coulomb's constant depend on energy, are considered and their propagators determined. From their spectral decomposition, we have found that the wave functions extracted are correctly normalized.

Comment on “Wave functions of a time-dependent harmonic oscillator in a static magnetic field”

2006 ◽  
Vol 73 (1) ◽  
Author(s):  
M. Maamache ◽  
A. Bounames ◽  
N. Ferkous
Keyword(s):  
Magnetic Field ◽  
Harmonic Oscillator ◽  
Static Magnetic Field ◽  
Wave Functions ◽  
Time Dependent

Exact wave functions and nonadiabatic Berry phases of a time-dependent harmonic oscillator

1995 ◽  
Vol 52 (4) ◽  
pp. 3352-3355 ◽  
Author(s):  
Jeong-Young Ji ◽  
Jae Kwan Kim ◽  
Sang Pyo Kim ◽  
Kwang-Sup Soh
Keyword(s):  
Harmonic Oscillator ◽  
Wave Functions ◽  
Time Dependent ◽  
Berry Phases

scholarly journals Occupation probability of harmonic-oscillator quanta for microscopic cluster-model wave functions

1996 ◽  
Vol 54 (4) ◽  
pp. 2073-2076 ◽  
Author(s):  
Y. Suzuki ◽  
K. Arai ◽  
Y. Ogawa ◽  
K. Varga
Keyword(s):  
Harmonic Oscillator ◽  
Cluster Model ◽  
Wave Functions ◽  
Occupation Probability ◽  
Model Wave
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