相关论文: Equivalence of two alternative approaches to Schro…

It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrodinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying…

We show that the Riccati form of the Schrodinger equation can be reformulated in terms of two linear equations depending on an arbitrary function G. When $G$ and the potential are polynomials, the solutions of these two equations are entire…

For the first time, Schr\"odinger equations with cubic and more complex nonlinearities containing the unknown function with constant delay are analyzed. The physical considerations that can lead to the appearance of a delay in such…

By their very nature, field-theoretical Hamiltonians are derived in momentum representation. To solve the corresponding integro-differential equations is more difficult than to solve the simpler differential equations in configuration space…

We obtained a new class of exactly-solvable potentials by means of the hypergeometric equation for Schrodinger equation, which different from the exactly-solvable potentials introduced by Bose and Natanzon. Using the new class of solvable…

The direct and inverse scattering problems on the full line are analyzed for a first-order system of ordinary linear differential equations associated with the derivative nonlinear Schr\"odinger equation and related equations. The system…

The present article deals with the similarity method to tackle the fractional Schrodinger equation where the derivative is defined in the Riesz sense. Moreover the procedure of reducing a fractional partial differential equation (FPDE) into…

Recently developed supersymmetric perturbation theory has been successfully employed to make a complete mathematical analysis the reason behind exact solvability of some non-central potentials. This investigation clarifies once more the…

Infinite families of quasi-exactly solvable position-dependent mass Schr\"odinger equations with known ground and first excited states are constructed in a deformed supersymmetric background. The starting points consist in one- and…

Using similarity transformations we construct explicit solutions of the nonlinear Schrodinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their…

The independent solutions of the one-dimensional Schr\"odinger equation are approximated by means of the explicit summation of the leading constituent WKB series. The continuous matching of the particular solutions gives the uniformly valid…

The inherently homogeneous stationary-state and time-dependent Schroedinger equations are often recast into inhomogeneous form in order to resolve their solution nonuniqueness. The inhomogeneous term can impose an initial condition or, for…

We obtain novel nonlinear Schr\"{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential…

The complete solutions of the Schr\"odinger equation for a particle with time-dependent mass moving in a time-dependent linear potential are presented. One solution is based on the wave function of the plane wave, and the other is with the…

We propose a general method for constructing quasi-exactly solvable potentials with three analytic eigenstates. These potentials can be real or complex functions but the spectrum is real. A comparison with other methods is also performed.

We analyze a recent pedagogical proposal for an alternative treatment of the angular part of the Schr\"odinger equation with a central potential. We show that the authors' arguments are unclear, unconvincing and misleading.

The present article discusses the connection between exactly-solvable Schrodinger equations and the Liouville transformation. This transformation yields a large class of exactly-solvable potentials, including the exactly-solvable potentials…

We apply the principles discussed in an earlier paper to the construction of discrete time field theories. We derive the discrete time field equations of motion and Noether's theorem and apply them to the Schrodinger equation to illustrate…

We construct a general algorithm generating the analytic eigenfunctions as well as eigenvalues of one-dimensional stationary Schroedinger Hamiltonians. Both exact and quasi-exact Hamiltonians enter our formalism but we focus on quasi-exact…

The general solution of SUSY intertwining relations of first order for two-dimensional Schr\"odinger operators with position-dependent (effective) mass is built in terms of four arbitrary functions. The procedure of separation of variables…