scholarly journals Multi-band structure of a coupling constant for quantum bound states of a generalized nonlinear Schrödinger model

2005 ◽  
Vol 341 (5-6) ◽  
pp. 371-379 ◽  
Author(s):  
B. Basu-Mallick ◽  
Tanaya Bhattacharyya ◽  
Diptiman Sen
Keyword(s):  
Band Structure ◽  
Bound States ◽  
Coupling Constant ◽  
Nonlinear Schrödinger ◽  
Multi Band

scholarly journals QUANTUM BOUND STATES FOR A DERIVATIVE NONLINEAR SCHRÖDINGER MODEL AND NUMBER THEORY

2004 ◽  
Vol 19 (36) ◽  
pp. 2697-2706 ◽  
Author(s):  
B. BASU-MALLICK ◽  
TANAYA BHATTACHARYYA ◽  
DIPTIMAN SEN
Keyword(s):  
Number Theory ◽  
Binding Energy ◽  
Continued Fractions ◽  
Bound States ◽  
Coupling Constant ◽  
Nonlinear Schrödinger ◽  
Farey Sequences ◽  
Negative Binding Energy

A derivative nonlinear Schrödinger model is shown to support localized N-body bound states for several ranges (called bands) of the coupling constant η. The ranges of η within each band can be completely determined using number theoretic concepts such as Farey sequences and continued fractions. For N≥3, the N-body bound states can have both positive and negative momenta. For η>0, bound states with positive momentum have positive binding energy, while states with negative momentum have negative binding energy.

Dynamical variables in the Bethe-Salpeter formalism

1955 ◽  
Vol 233 (1193) ◽  
pp. 248-266 ◽  
Keyword(s):  
Matrix Element ◽  
Bound States ◽  
Dynamical Variable ◽  
Wave Functions ◽  
Coupling Constant ◽  
Scattering States ◽  
The Matrix ◽  
The Masses

It is shown that a knowledge of the behaviour of the propagators around their singularities enables one to determine not only the masses of bound states, but also the matrix element of any dynamical variable between two bound states. One is thus enabled to find such a matrix element, to any order in the coupling constant, by the integration of certain expressions over the corresponding Bethe-Salpeter wave-functions. As a consequence, it is possible to find normalization and orthogonality properties of these wave-functions, which in turn lead to the condition which must be imposed on their singularities a t the origin. More light is thus shed on Goldstein’s difficulty concerning the existence of a continuous infinity of bound states. The formalism is extended to scattering states in which some of the particles may be composite—in particular, an expression for the S -matrix is obtained

scholarly journals Bound states and band structure—A unified treatment through the quantum Hamilton–Jacobi approach

2005 ◽  
Vol 320 (1) ◽  
pp. 164-174 ◽  
Author(s):  
S. Sree Ranjani ◽  
A.K. Kapoor ◽  
P.K. Panigrahi
Keyword(s):  
Band Structure ◽  
Bound States
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