Related papers: Schroedinger difference equation with deterministi…
We show that solutions of the Schr\"odinger equation with a symmetric P\"oschl-Teller potential of a particular form can be expressed in terms of a closed combination (not series) of trigonometric functions. Using some properties of the…
This paper mainly addresses the strong unique continuation property for the electromagnetic Schr\"{o}dinger operator with complex-valued coefficients. Appropriate multipliers with physical backgrounds have been introduced to prove a priori…
Exact analytic solutions to the Schr\"odinger equation for an electron moving in three dimensional potentials have been studied. These solutions can correspond to metals, semiconductors, or insulators. We show that there is an efficient…
S-state Bound state solution to Schroedinger equation for an exponential potential is derived using the Mellin transform. This method is a new and an alternative to the usual method of reducing Schroedinegr equation to a Bessel differential…
The Hamiltonian for a particle constrained to motion near a toroidal helix with loops of arbitrary eccentricity is developed. The resulting three dimensional Schr\"odinger equation is reduced to a one dimensional effective equation…
Exact solutions of Schrodinger equation for PT-/non-PT-symmetric and non-Hermitian Morse and Poschl-Teller potentials are obtained with the position-dependent effective mass by applying a point canonical transformation method. Three kinds…
The Cauchy problem for the Schr\"odinger equations is studied with time-dependent potentials growing polynomially in the spatial direction. First the existence and the uniqueness of solutions are shown in the weighted Sobolev spaces. In…
We study positive bound states for the semiclassical stationary nonlinear Schr\"odinger equation. We are especially interested in solutions which concentrate on a lower dimensional sphere. We adopt a purely variational approach which allows…
We relax the regularity condition on potentials of the Schr\"odinger equation in uniqueness results on the inverse boundary value problem which were recently proved in [11] and [5].
We derive an effective equation for the dynamics of many identical bosons in dimension one in the presence of a tiny impurity. The interaction between every pair of bosons is mediated by the impurity through a positive three-body potential.…
This paper establishes new estimates for linear Schroedinger equations in R^3 with time-dependent potentials. Some of the results are new even in the time-independent case and all are shown to hold for potentials in scaling-critical,…
Analytical solutions to the time-dependent Shr\"{o}dinger equation in one dimension are developed for time-independent potentials, one consisting of an infinite wall and a repulsive delta function. An exact solution is obtained by means of…
We consider ergodic families of Schr\"odinger operators over base dynamics given by strictly ergodic subshifts on finite alphabets. It is expected that the majority of these operators have purely singular continuous spectrum supported on a…
We obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The…
We prove unique continuation properties for solutions of evolution Schr\"odinger equation with time dependent potentials. In the case of the free solution these correspond to uncertainly principles referred to as being of Morgan type. As an…
The free Schr\"odinger equation with mass M can be turned into a non-massive Klein-Gordon equation via Fourier transformation with respect to M. The kinematic symmetry algebra sch_d of the free d-dimensional Schr\"odinger equation with M…
Using first and second order supersymmetry formalism we obtain a class of exactly solvable potentials subject to moving boundary conditions.
We construct arbitrary-order Darboux transformations for Schroedinger equations with energy-dependent potential and position-dependent mass within the Dunkl formalism. Our construction is based on a point transformation that interrelates…
We construct a local in time, exponentially decaying solution of the one-dimensional variable coefficient Schrodinger equation by solving a nonstandard boundary value problem. A main ingredient in the proof is a new commutator estimate…
We study the Schr\"odinger bridge problem when the endpoint distributions are available only through samples. Classical computational approaches estimate Schr\"odinger potentials via Sinkhorn iterations on empirical measures and then…