7 citations · 18 across the 7 of their papers we have counts for
7 papers
Two new integrable cases of two-dimensional quantum mechanics with a magnetic field
Vladimir Marikhin
Two integrable cases of two-dimensional Schrödinger equation with a magnetic field are proposed. Using the polar coordinates and the symmetrical gauge, we will obtain solutions of…
On three-dimensional quasi-Stäckel Hamiltonians
V. G. Marikhin
A three-dimensional integrable generalization of the Stäckel systems is proposed. The classification of such systems is obtained which results in two families. The first one is the…
Quantum tops as examples of commuting differential operators
V. E. Adler, V. G. Marikhin, A. B. Shabat
We study the quantum analogs of tops on Lie algebras and represented by differential operators.
Pairs of commuting Hamiltonians quadratic in momenta
V. G. Marikhin, V. V. Sokolov
In the case of two degree system the pairs of quadratic in momenta Hamiltonians commuting according the standard Poisson bracket are considered. The new many-parametrical families…
Separation of variables on a non-hyperelliptic curve
V. G. Marikhin, V. V. Sokolov
In the paper we consider several dynamical systems that admit a separation of variables on the algebraic curve of genus 4. The main result of the paper is an explicit formula for t…
Integrable systems with quadratic nonlinearity in Fourier space
V. G. Marikhin
The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The famous systems of this type such…