On the higher-order deformed Heisenberg spin equation as an exactly solvable dynamical system

1989 ◽  
Vol 22 (21) ◽  
pp. 4735-4736 ◽  
Author(s):  
M Lakshmanan
Keyword(s):  
Dynamical System ◽  
Higher Order ◽  
Heisenberg Spin ◽  
Exactly Solvable ◽  
Spin Equation

Closed-form representations of iterated Darboux transformations for the massless Dirac equation

2021 ◽  
Vol 36 (08n09) ◽  
pp. 2150064
Author(s):  
Axel Schulze-Halberg
Keyword(s):  
Dirac Equation ◽  
Closed Form ◽  
Scalar Potential ◽  
Higher Order ◽  
Two Dimensional ◽  
Darboux Transformations ◽  
First Order ◽  
Dirac Systems ◽  
Form Representation ◽  
Exactly Solvable

It is shown that first-order Darboux transformations for the two-dimensional massless Dirac equation with scalar potential and for the Schrödinger equation are the same up to a change of coordinates. As a consequence, we obtain a closed-form representation of iterated, higher-order Darboux transformations for our Dirac equation. We use the formalism to generate several new exactly-solvable Dirac systems through higher-order Darboux transformations.

On relativistic gasdynamics: invariance under a class of reciprocal-type transformations and integrable Heisenberg spin connections

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200487
Author(s):  
C. Rogers ◽  
T. Ruggeri ◽  
W. K. Schief
Keyword(s):  
Conservation Laws ◽  
Classical Limit ◽  
Three Dimensional ◽  
Classical System ◽  
Two Dimensional ◽  
Stationary Case ◽  
Heisenberg Spin ◽  
Lift And Drag ◽  
Spin Equation

A classical system of conservation laws descriptive of relativistic gasdynamics is examined. In the two-dimensional stationary case, the system is shown to be invariant under a novel multi-parameter class of reciprocal transformations. The class of invariant transformations originally obtained by Bateman in non-relativistic gasdynamics in connection with lift and drag phenomena is retrieved as a reduction in the classical limit. In the general 3+1-dimensional case, it is demonstrated that Synge’s geometric characterization of the pressure being constant along streamlines encapsulates a three-dimensional extension of an integrable Heisenberg spin equation.

scholarly journals MATCHING WEAK COUPLING AND QUASICLASSICAL EXPANSIONS FOR DUAL QES PROBLEMS

2002 ◽  
Vol 17 (31) ◽  
pp. 4661-4667 ◽  
Author(s):  
MICHAEL KAVIC
Keyword(s):  
Energy Level ◽  
Weak Coupling ◽  
Energy Levels ◽  
Higher Order ◽  
Wkb Approximation ◽  
Reflection Property ◽  
Exactly Solvable

Certain quasi-exactly solvable systems exhibit an energy reflection property that relates the energy levels of a potential or of a pair of potentials. We investigate two sister potentials and show the existence of this energy reflection relationship between the two potentials. We establish a relationship between the lowest energy edge in the first potential using the weak coupling expansion and the highest energy level in the sister potential using a WKB approximation carried out to higher order.

Sign in / Sign up

Export Citation Format

Share Document