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

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.

Author(s):  
Jacqueline A. Stedall

Following the discussion of Brouncker's work on quadrature, rectification and continued fractions in Part I of this paper, Part II analyses the disputes between Brouncker and Wallis in England and Fermat in France over problems in what would now be called number theory. Contemporary and later observers regarded Brouncker and Wallis as equally responsible for the English contribution, but it was Brouncker who took the greater interest in Fermat's challenges and who produced the more sophisticated solutions. The paper ends with an assessment of Brouncker's contribution to mathematics and argues that his contemporary reputation was well deserved and his mathematics of lasting value.


Sign in / Sign up

Export Citation Format

Share Document