Time Dependent Supersymmetry in Quantum Mechanics

The well-known supersymmetric constructions such as Witten's supersymmetric quantum mechanics, Spiridonov-Rubakov parasupersymmetric quantum mechanics, and higher-derivative SUSY of Andrianov et al. are extended to the nonstationary Schr\"odinger equation. All these constructions are based on the time-dependent Darboux transformation. The superalgebra over the conventional Lie algebra is constructed. Examples of time-dependent exactly solvable potentials are given.Comment: Talk given at the 7-th Lomonosov Conference "Problems of Fundamental Physics", 24-30 August, 1995, see proceedings book (with the minor corrections) Moscow, 1997, p. 54-6

Planar channelling of relativistic electrons in half-wave silicon crystal and corresponding radiation

New experimental data on planar channeling of 255 MeV electrons in a 0.74 µm Si Half-Wave Crystal (HWC) obtained at SAGA-LS facility are presented. The computer simulation showed that the angular distribution of electrons after penetration through the HWC revealed the number of unknown before peculiarities is connected with specific electron trajectories in HWC. These specific trajectories lead to specific radiation, the properties of which are analyzed

Transmutations for Darboux transformed operators with applications

We solve the following problem. Given a continuous complex-valued potential q_1 defined on a segment [-a,a] and let q_2 be the potential of a Darboux transformed Schr\"odinger operator. Suppose a transmutation operator T_1 for the potential q_1 is known such that the corresponding Schr\"odinger operator is transmuted into the operator of second derivative. Find an analogous transmutation operator T_2 for the potential q_2. It is well known that the transmutation operators can be realized in the form of Volterra integral operators with continuously differentiable kernels. Given a kernel K_1 of the transmutation operator T_1 we find the kernel K_2 of T_2 in a closed form in terms of K_1. As a corollary interesting commutation relations between T_1 and T_2 are obtained which then are used in order to construct the transmutation operator for the one-dimensional Dirac system with a scalar potential

On the wave zone of synchrotron radiation

The extension of the wave zone of synchrotron radiation is studied

Squaring the Dirac equations

A complete solution of the problem of squaring the Dirac equation with arbitrary external electromagnetic field is expounded