Related papers: Numerov and phase-integral methods for charmonium
The master equation for a charged harmonic oscillator coupled to an electromagnetic reservoir is investigated up to fourth-order in the interaction strength by using Krylov averaging method. The interaction is in the velocity-coupling form…
We present a stochastic method for solving the time-dependent Schr\"odinger equation, generalizing a ground-state full configuration interaction Quantum Monte Carlo method. By performing the time-integration in the complex plane close to…
From the mathematical side, nonlinear Schr\"odinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome this problem by focusing on spherically symmetric…
We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a…
By using the recent mathematical tools developed in quaternionic differential operator theory, we solve the Schroedinger equation in presence of a quaternionic step potential. The analytic solution for the stationary states allows to…
We extend the quantization \`a la Faddeev-Jackiw for non-autonomous singular systems. This leads to a generalization of the Schr\"odinger equation for those systems. The method is exemplified by the quantization of the damped harmonic…
This paper is concerned with the final state problem for the homogeneous type nonlinear Schr\"odinger equation with time-decaying harmonic potential. The nonlinearity has the critical order and is not necessarily the form of a polynomial.…
In this paper we present two optimized eight-step symmetric implicit methods with phase-lag order ten and infinite (phase-fitted). The methods are constructed to solve numerically the radial time-independent Schr\"odinger equation with the…
In the present paper we introduce a new methodology for the construction of numerical methods for the approximate solution of the one-dimensional Schr\"odinger equation. The new methodology is based on the requirement of vanishing the…
In this paper, we establish refined Strichartz estimates for higher-order Schr\"odinger equations with initial data exhibiting partial regularity. By partial regularity, we mean that the initial data are not required to have full Sobolev…
We focus on the ground state of the cubic-quintic nonlinear Schr\"{o}dinger energy functional \begin{gather*} \begin{aligned} {E}(\varphi)=\frac{1}{2}\int_{\mathbb{R}^d}\left(|\nabla \varphi|^2+V(x)|\varphi|^2\right)\,dx…
A variationally improved Sturmian approximation for solving time-independent Schr\"odinger equation is developed. This approximation is used to obtain the energy levels of a quartic anharmonic oscillator, a quartic potential, and a Gaussian…
The general formulation of a technically advantageous method to find the ground state solution of the Schrodinger equation in configuration space for systems with a number of particles A greater than 4 is presented. The wave function is…
We review and compare different variational formulations for the Schr\"{o}dinger field. Some of them rely on the addition of a conveniently chosen total time derivative to the hermitic Lagrangian. Alternatively, the Dirac-Bergmann algorithm…
We prove existence and multiplicity of bound and ground state solutions, under appropriate conditions on the parameters, for a bi-harmonic stationary system of coupled nonlinear Schr\"odinger--Korteweg-de Vries equations.
The Schr\"odinger equation with a harmonic potential coupled to the Poisson equation, called the Schr\"odinger-Newton-Hooke (SNH) system, has been considered in a variety of physical contexts, ranging from quantum mechanics to general…
The Schroedinger equation is solved for an A-nucleon system using an expansion of the wave function in nonsymmetrized hyperspherical harmonics. Our approach is both an extension and a modification of the formalism developed by Gattobigio et…
In this work, we develop a theoretical description of the collective behavior of interacting dipolar planar rotors by using time independent perturbation theory and a small angle quadratic approximation. The ground state properties for both…
In this paper, we propose an iterative method to compute the positive ground states of saturable nonlinear Schr\"odinger equations. A discretization of the saturable nonlinear Schr\"odinger equation leads to a nonlinear algebraic eigenvalue…
We develop an efficient numerical method to study the quantum critical behavior of disordered systems with $\mathcal{O}(N)$ order-parameter symmetry in the large$-N$ limit. It is based on the iterative solution of the large$-N$ saddle-point…