Related papers: Some special solutions of the Schroedinger equatio…
We look for positive solutions to the nonlinear Schrodinger equation with a potential, under the hypothesis of zero mass on the nonlinearity, in a particular situation. Existence and multiplicity results are provided.
An infinite family of closed-form solutions is exhibited for the Schroedinger equation for the potential $V(r) = -Z/\sqrt{|r|^{2} + a^{2}}$. Evidence is presented for an approximate dynamical symmetry for large values of the angular…
We present some recent results on the existence of solutions of the Schr\"odinger flows, and pose some problems for further research.
The general solution of the one-dimensional stationary Schroedinger equation in the form of a formal power series is considered. Its efficiency for numerical analysis of initial value and boundary value problems is discussed.
We study a class of logarithmic Schrodinger equations with periodic potential which come from physically relevant situations and obtain the existence of infinitely many geometrically distinct solutions.
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
A five-dimensional symmetry algebra consisting of Lie point symmetries is firstly computed for the nonlinear Schroedinger equation, which, together with a reflection invariance, generates two five-parameter solution groups. Three ansaetze…
We give a logically and mathematically self-consistent procedure of quantization of free scalar field, including quantization on space-like surfaces. A short discussion of possible generalization to interacting fields is added.
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
We discuss a new approach to solve the low lying states of the Schroedinger equation. For a fairly large class of problems, this new approach leads to convergent iterative solutions, in contrast to perturbative series expansions. These…
An algebraic method of constructing potentials for which the Schroedinger equation with position dependent mass can be solved exactly is presented. A general form of the generators of su(1,1) algebra has been employed with a unified…
The method of solving of nonlinear Schr\"odinger equation is considered. Some examples of its applications are demonstrated.
An algorithm is proposed for research into the symmetrical properties of theoretical and mathematical physics equations. The application of this algorithm to the free Schrodinger equation permited us to establish that in addition to the…
We present a class of confining potentials which allow one to reduce the one-dimensional Schroodinger equation to a named equation of mathematical physics, namely either Bessel's or Whittaker's differential equation. In all cases, we…
We solve the one-dimensional Schr\"odinger equation for the bound states of two potential models with a rich structure as shown by their "spectral phase diagram". These potentials do not belong to the well-known class of exactly solvable…
A new family of solvable potentials related to the Schroedinger-Riccati equation has been investigated. This one-dimensional potential family depends on parameters and is restricted to the real interval. It is shown that this potential…
Maximal estimates for Schr\"odinger means and convergence almost everywhere of sequences of Schr\"odinger means are studied.
We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is…
A class of generalized Schr\"{o}dinger problems in bounded domain is studied. A complete overview of the set of solutions is provided, depending on the values assumed by parameters involved in the problem. In order to obtain the results, we…
A closed expression for the harmonic oscillator wave function after the passage of a linear signal with arbitrary time dependence is derived. Transition probabilities are simple to express in terms of Laguerre polynomials. Spontaneous…