Related papers: Eigenvalue Problem in Two Dimension for An Irregul…
Violation of Lorentz invariancy in the high energy quantum gravity motivates one to consider an energy dependent spacetime with massive deformation of standard general relativity. In this paper, we take into account an energy dependent…
I develop the solution to the problem of an electron confined in a composite quadratic well subject to a simple, external periodic force. The method of solution illustrates several of the basic techniques useful in formally solving the…
We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman-Schwinger bound in three dimensions. Specifically, counting…
Random Schroedinger operators with imaginary vector potentials are studied in dimension one. These operators are non-Hermitian and their spectra lie in the complex plane. We consider the eigenvalue problem on finite intervals of length n…
We calculate accurate eigenvalues and eigenfunctions of the Schr\"odinger equation for a two-dimensional quantum dipole. This model proved useful for the study of elastic effects of a single edge dislocation. We show that the Rayleigh-Ritz…
We present a fully analytic approach for evaluating boundary integrals in two dimensions for Smoothed Particle Hydrodynamics (SPH). Conventional methods often rely on boundary particles or wall re-normalization approaches derived from…
The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local…
We study bound states of the two-dimensional Helmholtz equations with Dirichlet boundary conditions in an open geometry given by two straight leads of the same width which cross at an angle $\theta$. Such a four-terminal junction with a…
For Klein-Gordon equation a consistent physical interpretation of wave functions is reviewed as based on a proper modification of the scalar product in Hilbert space. Bound states are then studied in a deep-square-well model where spectrum…
The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically…
We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two…
The model of a two-electron quantum dot, confined to move in a two dimensional flat space, is revisited. Generally, it is argued that the solutions of this model obtained by solving a biconfluent Heun equation have some limitations. In…
The complex Helmholtz equation $(\Delta + k^2)u=f$ (where $k\in{\mathbb R},u(\cdot),f(\cdot)\in{\mathbb C}$) is a mainstay of computational wave simulation. Despite its apparent simplicity, efficient numerical methods are challenging to…
We study a two-phase free boundary problem in which the two-phases satisfy an impenetrability condition. Precisely, we have two ordered positive functions, which are harmonic in their supports, satisfy a Bernoulli condition on the one-phase…
We theoretically study the subband structure of single Si $\delta$-doped GaAs inserted in a quantum well and subject to an electric field applied along the growth direction. We use an efficient self-consistent procedure to solve…
Due to the absence of degeneracy in one dimension, when a parameter, $\lambda$, of a potential is varied slowly the discrete energy eigenvalue curves, $E_n(\lambda)$, cannot cross but they are allowed to come quite close and diverge from…
In this paper, we investigated the Pauli equation in a two-dimensional noncommutative phase-space by considering a constant magnetic field perpendicular to the plane. We mapped the noncommutative problem to the equivalent commutative one…
A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the…
We study a Bose-Einstein condensate in a PT-symmetric double-well potential where particles are coherently injected in one well and removed from the other well. In mean-field approximation the condensate is described by the Gross-Pitaevskii…
We study, in the paradigm of open quantum systems, the dynamics of quantum coherence of a static polarizable two-level atom which is coupled with a thermal bath of fluctuating electromagnetic field in the absence and presence of boundaries.…