Related papers: Analytical solutions for the Schr\"odinger equatio…
In this paper, a nonlinear Schr\"odinger equation with an attractive (focusing) delta potential and a repulsive (defocusing) double power nonlinearity in one spatial dimension is considered. It is shown, via explicit construction, that both…
We obtain exact solutions of Dirac equation at zero kinetic energy for radial power-law relativistic potentials. It turns out that these are the relativistic extension of a subclass of exact solutions of Schrodinger equation with two-term…
We find exact solutions of the time-dependent Schr\"odinger equation for a family of quasi-exactly solvable time-dependent potentials by means of non-unitary gauge transformations.
In this paper, we use the variational method, especially the perturbation method, to find the perturbed high energy solutions of the quadratic coupled Schrodinger system with asymmetric asymptotic potential and their asymptotic behavior as…
The recently introduced scheme [20,21] is extended to propose an algebraic non-perturbative approach for the analytical treatment of Schr\"odinger equations with non-solvable potentials involving an exactly solvable potential form together…
By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrodinger equation for the pseudoharmonic and Kratzer potentials in two dimensions. The energy levels of all the bound states are…
We present general results on exponential decay of finite energy solutions to stationary nonlinear Schr\"odinger equations.
In this paper we present a novel multiscale splitting approach to solve multiscale Schroedinger equation, which have large different time-scales. The energy potential is based on highly oscillating functions, which are magnitudes faster…
In this work, we analytically study the Schr\"odinger equation for the (non-pure) dipolar ion potential V (r) = q/r + Dcos{\theta}/r 2 , in the case of 2D systems using the separation of variables and the Mathieu equations for the angular…
We consider the semilinear electromagnetic Schr\"{o}dinger equation (-i\nabla+A(x))^{2}u + V(x)u = |u|^{2^{\ast}-2}u, u\in D_{A,0}^{1,2}(\Omega,\mathbb{C}), where $\Omega=(\mathbb{R}^{m}\smallsetminus{0})\times\mathbb{R}^{N-m}$ with $2\leq…
The classical Schr\"odinger equation with a harmonic trap potential $V(x)=|x|^2$, describing the quantum harmonic oscillator, has been studied quite extensively in the last twenty years. Its ground states are bell-shaped and unique, among…
The convergent iterative procedure for solving the groundstate Schroedinger equation is extended to derive the excitation energy and the wave function of the low-lying excited states. The method is applied to the one-dimensional quartic…
We deal with the exact solutions of Schrodinger equation characterized by position-dependent effective mass via point canonical transformations. The Morse, Poschl-Teller and Hulthen type potentials are considered respectively. With the…
As a simple model for lattice defects like grain boundaries in solid state physics we consider potentials which are obtained from a periodic potential $V = V(x,y)$ on $\R^2$ with period lattice $\Z^2$ by setting $W_t(x,y) = V(x+t,y)$ for $x…
We relax the usual diagonal constraint on the matrix representation of the eigenvalue wave equation by allowing it to be tridiagonal. This results in a larger solution space that incorporates an exact analytic solution for the non-central…
We consider the nonlinear Schr\"{o}dinger equation $-\Delta u + V(x) u = \Gamma(x) |u|^{p-1}u$ in $\R^n$ where the spectrum of $-\Delta+V(x)$ is positive. In the case $n\geq 3$ we use variational methods to prove that for all $p\in…
We consider series solutions of the Schr\"odinger equation for the Bender-Boettcher potentials V(x)=-(ix)^N with integer N. A simple truncation is introduced which provides accurate results regarding the ground state and first few excited…
In this work, the analytical solutions of the $D$-dimensional Schr\"odinger equation are studied in great detail for the Wood-Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount…
The second order $N$-dimensional Schr\"odinger equation with pseudoharmonic potential is reduced to a first order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution…
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…