HYDROGEN ATOM AND SPHERICAL HARMONICS

Hossein Fakhri, B. Mojaveri

The associated Legendre functions [Formula: see text] for a given l-m, may be taken into account as the increasing infinite sequences with respect to both indices l and m. This allows us to construct the exponential generating functions for them in two different methods by using Rodrigues formula. As an application then we present a scheme to construct generalized coherent states corresponding to the spherical harmonics [Formula: see text].

Cynthia Kolb Whitney

Ghada E. S. Elammeen Amna E. Musa

The solution of radial Schrödinger equation for hydrogen like atoms is complex. One needs simple solution the behavior of nano particle needs also to be described. Nano spherical particles are isolated non interacting particles that obey quantum laws. Thus one expects their behavior to resemble that of particles in a box, or hydrogen like atoms. The spherical nano shape requires using spherical coordinate to solve Schrödinger Equation. The solution found that the wave function is diminishing outside the sphere, which agrees with observations. This solution is simpler than the conventional one, where it is a sum of sine and cosine function.

Edgard Elbaz

Weixing Qu, HU SU-XING, XU ZHI-ZHAN +1 more

The process of harmonic generation for a two-level atom is investigated theoretically.The model of oscillator driven by a nonlinear external force is used to simulate an induced porlarization of the atom,and the characteristics in harmonic spectrum of the atom are analyzed for a weak and a super-intense laser pulses.

Andrey G. Grozin