On the question of extended two-dimensional non-relativistic supersymmetry
An algorithm for realizing the algebra of two-dimensional supersymmetric quantum mechanics is described. The cases N = 2 and N = 3 are described in detail. The procedure for iterating Darboux transformations is considered separately. In contrast to the one-dimensional case, in which the problem is completely solved by Krum's formulas, iterations of two-dimensional Darboux transformations remain insufficiently understood.
Yurova A. A., Chirikov R. V.
supersymmetry, Darboux transform, 2D-Hamiltonian...
Two-dimensional supersymmetric quantum mechanics and the Moutard transformations
This is a treatise on a two-dimensional supersymmetric hamiltonian H whose components consists of two scalar (h0, h1) and one matrix-valued hml quantum-mechanical Hamiltonians with constant terms added to the mix. In particular, the article discusses the ways to utilize a known solution of the spectral problem for operator h0 in the multi-dimensional generalization of the factorization method in order to pro-duce such hml and h1 that their ground-state eigenvalues will be identical to each...
New classes of exact solutions and consistent models of cosmological evolution
A method for construction of exact cosmological solutions of Einstein equations is developed. The method is based on representation of these equations as a second-order linear differential equation. Particularly, the method allows to construct a more general solution, parametrized by two constants, using any known solution. Also it is shown, that in a specific case new classes of exact solutions have singularities with the following property: a geodesic, which begins or ends in the singularity, has...