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 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

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.

scholarly journals Accurate study from adaptive perturbation method

2021 ◽  
pp. 2150029
Author(s):  
Chen-Te Ma
Keyword(s):  
Exact Solution ◽  
Harmonic Oscillator ◽  
Perturbation Method ◽  
Particle Physics ◽  
Higgs Field ◽  
Mass Term ◽  
Coupling Constants ◽  
Position Operator ◽  
Leading Order ◽  
Fock State

The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and nondiagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants. We study the harmonic oscillator with the interacting potential, [Formula: see text], where [Formula: see text] and [Formula: see text] are coupling constants, and [Formula: see text] is the position operator. In this study, each perturbed term has an exact solution. We demonstrate the accurate study of the spectrum and [Formula: see text] up to the next leading-order correction. In particular, we study a similar problem of Higgs field from the inverted mass term to demonstrate the possible nontrivial application of particle physics.

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