Search

Maximal kinematical invariance groups of the Schrödinger equations with position dependent mass (PDM) and arbitrary potential are classified. It is demonstrated that there exist seven classes of such equations possessing non-equivalent continuous symmetry group. Three of these classes include arbitrary functions while the remaining ones are defined up to arbitrary parameters. In particular, for the case of a constant mass the class missing in the Boyer classification (Boyer 1974 Helv. Phys. Acta.47 450) is indicated. A constructive test of (non)equivalence of a PDM system to a constant mass system is proposed. [ABSTRACT FROM AUTHOR]

Second order integrals of motion for 3d quantum mechanical systems with position dependent masses (PDM) are classified. Namely, all PDM systems are specified which, in addition to their rotation invariance, admit at least 1 second order integral of motion. All such systems appear to be also shape invariant and exactly solvable. Moreover, some of them possess the property of double shape invariance and can be solved using two different superpotentials. Among them there are systems with double shape invariance which present nice bridges between the Coulomb and isotropic oscillator systems. A simple algorithm for calculating the discrete spectrum and the corresponding state vectors for the considered PDM systems is presented and applied to solve five of the found systems. [ABSTRACT FROM AUTHOR]

Superintegrable d-dimensional quantum mechanical systems with spin, which admit a generalized Laplace–Runge–Lenz vector are presented. The systems with spins 0, and 1 are considered in detail. All these systems are exactly solvable for arbitrary d, and their solutions are presented explicitly. [ABSTRACT FROM AUTHOR]

A constructive approach to the theory of diffusion processes is proposed, which is based on application of both symmetry analysis and the method of modelling functions. An algorithm for construction of the modelling functions is suggested. This algorithm is based on the error function expansion (ERFEX) of experimental concentration profiles. The high-accuracy analytical description of the profiles provided by ERFEX approximation allows a convenient extraction of the concentration dependence of diffusivity from experimental data and prediction of the diffusion process. Our analysis is exemplified by its employment in experimental results obtained for surface diffusion of lithium on the molybdenum (1 1 2) surface precovered with dysprosium. The ERFEX approximation can be directly extended to many other diffusion systems. [ABSTRACT FROM AUTHOR]