Closed-form solutions of the Schroedinger equation for a class of smoothed Coulomb potentials

An Efficient and Accurate Grid Method for Solving the Time-Dependent Schroedinger Equation: Application of Coulomb Wave Function DVR to Atomic Systems in Strong Laser Fields

We present an efficient and accurate grid method for solving the time-dependent Schrödinger equation of atomic systems interacting with intense laser pulses. As usual, the angular part of the wave function is expanded in terms of spherical harmonics. Instead of the usual finite difference (FD) scheme, the radial coordinate is discretized using the discrete variable representation which is constructed from the Coulomb wave function. For an accurate description of the ionization dynamics of atomic systems, the Coulomb wave function discrete variable representation (CWDVR) method needs 3-10 times…

Generalized quantum mechanical two Coulomb centers problem (Demkov problem)

We present a new exactly solvable quantum problem for which the Schroedinger equation allows for separation of variables in oblate spheroidal coordinates. Namely, this is the quantum mechanical two Coulomb centers problem for the case of imaginary intercenter parameter and complex conjugate charges is considered. Since the potential is defined by the two-sheeted mapping whose singularities are concentrated on a circle rather than at separate points, there arise additional possibilities in choice of boundary conditions. Detailed classification of the various types of boundary-value problems is …

Soft-core Coulomb potentials and Heun's differential equation

Schroedinger's equation with the attractive potential V(r) = -Z/(r^q+ b^q)^(1/q), Z > 0, b > 0, q >= 1, is shown, for general values of the parameters Z and b, to be reducible to the confluent Heun equation in the case q=1, and to the generalized Heun equation in case q=2. In a formulation with correct asymptotics, the eigenstates are specified a priori up to an unknown factor. In certain special cases this factor becomes a polynomial. The Asymptotic Iteration Method is used either to find the polynomial factor and the associated eigenvalue explicitly, or to construct accurate approximations f…

不看好Schroedinger-Newton方程

Disfavoring the Schroedinger-Newton equation

本文通过在氢原子的Schroedinger-Newton方程中加入电自相互作用项，发现单电子电磁自相互作用被排除，并指出需接近Planck尺度才能可靠测试该方程，从而基于低能下引力和电磁相互作用的相似性对其前景表示不看好。

Effects of the interaction between the magnetic moments of the proton and electron on the energy states of hydrogen atom

We make a comparison between the energy levels of the hydrogen atom, calculated by using standard methods, and that by using a modified Coulomb potential due to the interaction between the magnetic moments of the proton and electron. In this later method we use to ways. One is that in which we solve the Schroedinger equation with the modified Coulomb potential and some constraint conditions. The other is that in which we expand the modified Coulomb potential in Taylor series. The obtained results show that the first way gives a better agreement with experimental data.

Singularity Structures in Coulomb-Type Potentials in Two Body Dirac Equations of Constraint Dynamics

Two Body Dirac Equations (TBDE) of Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. Coulomb-type potentials in these applications lead naively in other approaches to singular relativistic corrections at short distances that require the introduction of either perturbative treatments or smoothing parameters. We examine the corresponding singular structures in the effective potentials of the relativistic Schroedinger equation obtained from the Pauli reduction of the TBDE. We find that the relativ…