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



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.


dressing method quantum operators Hopf equation eikonal equation 


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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRASMoscowRussia

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