This article is cited in 1 paper

Solutions of two-dimensional Schrödinger-type equations in a magnetic field

V. G. Marikhin

Landau Institute for Theoretical Physics, RAS, Moscow, Russia

Abstract: We use the method of dressing by a linear operator of general form to construct new solutions of Schrödinger-type two-dimensional equations in a magnetic field. In the case of a nonunit metric, we integrate the class of solutions that admit a variable separation before dressing. In particular, we show that the ratio of the coefficients of the differential operators in the unit metric case satisfies the Hopf equation. We establish a relation between the solutions of the two-dimensional eikonal equation with the unit right-hand side and solutions of the Hopf equation.

Keywords: dressing method, quantum operators, Hopf equation, eikonal equation.

Received: 13.03.2011

DOI: 10.4213/tmf6676

 English version: Theoretical and Mathematical Physics, 2011, 168:2, 1041–1047

Bibliographic databases:

• 
• 
• 
•