scholarly journals Exact solution of a kind of n-dimensions non-spherical harmonic oscillator p otential

2003 ◽  
Vol 52 (8) ◽  
pp. 1858
Author(s):  
Long Chao-Yun ◽  
Chen Ming-Lun ◽  
Cai Shao-Hong
Keyword(s):  
Exact Solution ◽  
Harmonic Oscillator ◽  
Spherical Harmonic

Exact solution of the Faddeev equations for the harmonic oscillator ground state

1980 ◽  
Vol 22 (1) ◽  
pp. 284-286 ◽  
Author(s):  
J. L. Friar ◽  
B. F. Gibson ◽  
G. L. Payne
Keyword(s):  
Exact Solution ◽  
Harmonic Oscillator ◽  
Ground State ◽  
Faddeev Equations

Exact solution of the four-body Faddeev-Yakubovsky equations for the harmonic oscillator

1994 ◽  
Vol 50 (1) ◽  
pp. 38-47 ◽  
Author(s):  
Alexander L. Zubarev ◽  
Victor B. Mandelzweig
Keyword(s):  
Exact Solution ◽  
Harmonic Oscillator

scholarly journals EXACT SOLUTION OF THE SCHWINGER MODEL WITH COMPACT U(1)

2001 ◽  
Vol 16 (03) ◽  
pp. 121-133
Author(s):  
ROMÁN LINARES ◽  
LUIS F. URRUTIA ◽  
J. DAVID VERGARA
Keyword(s):  
Exact Solution ◽  
Harmonic Oscillator ◽  
Gauge Group ◽  
Electric Charge ◽  
Axial Current ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Zero Modes ◽  
Compact Gauge Group ◽  
Θ Vacuum

The exact solution of the Schwinger model with compact gauge group U(1) is presented. The compactification is imposed by demanding that the only surviving true electromagnetic degree of freedom c has angular character. Not surprisingly, this topological condition defines a version of the Schwinger model which is different from the standard one, where c takes values on the line. The main consequences are: The spectra of the zero modes is not degenerated and does not correspond to the equally spaced harmonic oscillator, both the electric charge and a modified gauge-invariant chiral charge are conserved (nevertheless, the axial-current anomaly is still present) and, finally, there is no need to introduce a θ-vacuum. A comparison with the results of the standard Schwinger model is pointed out along the text.

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