相关论文: Eigenvalue bounds in one dimensional Schrodinger's…
In this paper we consider the inverse boundary value problem for the Schr\"odinger equation with potential in $L^p$ class, $p>4/3$. We show that the potential is uniquely determined by the boundary measurements.
Spherical confinement in 3D harmonic, quartic and other higher oscillators of even order is studied. The generalized pseudospectral method is employed for accurate solution of relevant Schr\"odinger equation in an \emph{optimum,…
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…
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…
The Schroedinger equation with one and two dimensional potentials are solved in the frame work of the sl(2) Lie algebra. Eigenfunctions of the Schroedinger equation for various asymmetric double-well potentials have been determined and the…
We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible hamiltonians and corresponding solutions for a finite…
We analyze Schr\"odinger operators whose potential is given by a singular interaction supported on a sub-manifold of the ambient space. Under the assumption that the operator has at least two eigenvalues below its essential spectrum we…
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 justify the validity of the discrete nonlinear Schrodinger equation for the tight-binding approximation in the context of the Gross-Pitaevskii equation with a periodic potential. Our construction of the periodic potential and the…
The formulation of the eigenvalue problem for the Schr\"odinger equation is studied, for the numerical solution a new approach is applied. With the usual exponentially rising free-state asymptotical behavior, and also with a first order…
We prove Strichartz estimates for the Schroedinger equation with an electromagnetic potential, in dimension $n\geq3$. The decay and regularity assumptions on the potentials are almost critical, i.e., close to the Coulomb case. In addition,…
The evolution problem for a quantum particle confined in a 1D box and interacting with one fixed point through a time dependent point interaction is considered. Under suitable assumptions of regularity for the time profile of the…
In this work we shall review some of our recent results concerning unique continuation properties of solutions of Schr\"odinger equations. In this equations we include linear ones with a time depending potential and semi-linear ones.
The Schrodinger equation for a particle moving in a square well potential with BenDaniel - Duke boundary conditions is solved. Using algebraic approximations for trigonometric functions, the transcendental equations of the bound states…
We use special quadrature formulas for singular and hypersingular integral to numerically solve the Schr\"{o}dinger equation in momentum space with the linear confinement potential, Coulomb and Cornell potentials. It is shown that the…
In classical physics, there is a basic principle, namely "A particle cannot be located at the position of another one on the same time". Which consequences can be derived if this principle is transferred into quantum physics? For doing…
We prove exponential localization for the Schr\"odinger operator with a Poisson random potential at the bottom of the spectrum in any dimension. We also prove exponential localization in a prescribed interval for all large Poisson…
Recurrent representations for an electron transmission and reflection amplitudes for a one-dimensional chain are obtained. The linear differential equations for scattering amplitudes of an arbitrary potential are found.
We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for…
In this paper we propose the hyperbolic Schredinger equation (HS). The solution of the HS for a particle in a box is obtained. It is shown that for particles with m greater of Mp the energy spectrum is independent of the mass of particle.