scholarly journals Schrodinger Equation for the Hydrogen Atom - A Simplified Treatment

2008 ◽  
Vol 5 (3) ◽  
pp. 659-662 ◽  
Author(s):  
L. R. Ganesan ◽  
M. Balaji
Keyword(s):  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Polar Coordinates ◽  
Mechanical Problem ◽  
Mathematical Concepts ◽  
Simple Method ◽  
Cartesian Coordinates ◽  
Alternative Method ◽  
Normal Method

A simple method is presented here for solving the wave mechanical problem of the hydrogen atom. The normal method of converting the Cartesian coordinates into polar coordinates is tedious and also requires an understanding of the Legendre and Lagurre polynomials. In this paper we are using an alternative method, which requires only minimal familiarity with mathematical concepts and techniques.

Quantum mass of an electron in the hydrogen atom derived from the relativistically modified Schrödinger equation

2020 ◽  
Vol 33 (3) ◽  
pp. 355-357
Author(s):  
Noboru Kohiyama
Keyword(s):  
Electromagnetic Wave ◽  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Free Electron ◽  
Schrodinger Equation ◽  
Photon Emission ◽  
X Rays ◽  
Frequency Condition

In Bohr's theory, the photon emission or absorption by the hydrogen atom is expressed by the frequency condition. In the hydrogen atom, the eigenvalue of energy derived from the relativistically modified Schrödinger equation contains the quantum mass of an electron. The frequency condition is explained using this mass. The electromagnetic wave (e.g., X rays) emission from the highly accelerated free electron was thus predicted from this mass.

Simple method to incorporate nonparabolicity effects in the Schrödinger equation of a quantum dot

2007 ◽  
Vol 101 (9) ◽  
pp. 093715 ◽  
Author(s):  
F. M. Gómez-Campos ◽  
S. Rodríguez-Bolívar ◽  
J. E. Carceller
Keyword(s):  
Quantum Dot ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Simple Method

On exact analytical solutions for the few-particle Schrödinger equation. II. The ground state of helium

1982 ◽  
Vol 384 (1786) ◽  
pp. 89-105 ◽  
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Least Squares Method ◽  
Formal Solution ◽  
Order Perturbation ◽  
Polar Coordinates ◽  
Perturbation Equation ◽  
Similar Treatment ◽  
Partial Wave Expansion

Analytical methods for solving the Schrödinger equation directly can be applied to few-particle systems. This is illustrated by deriving a solution to the first-order perturbation equation for the ground state of helium. This solution is the in form of a partial wave expansion in spherical polar coordinates with Legendre polynomials as the angular functions. The radial functions include polynomials and exponential integral functions. Arbitrary parameters in the formal solution, associated with the square-integrability of the wavefunction, are identified. Their values are deter­mined by a least-squares method. The same arbitrary parameters occur in formal solutions of the higher-order perturbation equations. It is evident that a similar treatment can be applied to these equations, and to the eigenvalue problem.

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