The angular part of the Schrödinger equation for the hydrogen atom

2002 ◽  
Vol 70 (6) ◽  
pp. 569-569
Author(s):  
Paul Mazur
Keyword(s):  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Angular Part

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.

scholarly journals Hénon–Heiles interaction for hydrogen atom in phase space

2016 ◽  
Vol 31 (10) ◽  
pp. 1650046 ◽  
Author(s):  
J. S. da Cruz Filho ◽  
R. G. G. Amorim ◽  
S. C. Ulhoa ◽  
F. C. Khanna ◽  
A. E. Santana ◽  
...  
Keyword(s):  
Phase Space ◽  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Gauge Invariance ◽  
Schrodinger Equation ◽  
Physical Basis

Using elements of symmetry, as gauge invariance, several aspects of a Schrödinger equation represented in phase space are introduced and analyzed under physical basis. The hydrogen atom is explored in the same context. Then we add a Hénon–Heiles potential to the hydrogen atom in order to explore chaotic features.

scholarly journals COMPUTING THE COMPLEX RADIUS DEPENDENCY AND THE TWO ANGLES VERSUS TIME IN THE HYDROGEN ATOM

2021 ◽  
Vol 7 (2(38)) ◽  
pp. 21-24
Author(s):  
Evgeny Georgievich Yakubovsky
Keyword(s):  
Hydrogen Atom ◽  
Kinetic Energy ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Electrical Energy ◽  
Total Kinetic Energy ◽  
Definition Of

Using the definition of the velocity of vacuum particles or streamlines from the Schrödinger equation, it was possible to determine the dependence of the radius and two angles on time. In the general case, several complex values of the radius and two angles were obtained as a function of time. But using continuous coordinates, it was possible to determine the change in the complex radius and two angles for the hydrogen atom. The resulting total kinetic energy of the atom differs from its own electrical energy, which provides the radiation of the atom.

Eigenvalues of energy in j (l + 1/2, l ‐ 1/2) electron state in the hydrogen atom derived from the relativistically modified Schrödinger equation

2021 ◽  
Vol 34 (2) ◽  
pp. 111-115
Author(s):  
Noboru Kohiyama
Keyword(s):  
Wave Equation ◽  
Hydrogen Atom ◽  
Dirac Equation ◽  
Schrödinger Equation ◽  
Radio Wave ◽  
Schrodinger Equation ◽  
Electron State ◽  
Microwave Emission

In the hydrogen atom, the eigenvalues of energy in j (l + 1/2, l ‐ 1/2) electron state cannot be correctly evaluated from the nonrelativistic Schrödinger equation. In order to express the relativistic properties of the wave equation for a particle with 1/2 spin, the Schrödinger equation is relativistically modified. The modified Schrödinger equation is solved for consistency with the eigenvalues of electron's energy derived from the Dirac equation. Based on the consistency of their eigenvalues, the different electron state is expressed. The microwave emission (e.g., 21 cm radio wave) by the hydrogen atom was thus predicted from this state.

scholarly journals METODE ELEMEN HINGGA UNTUK PENYELESAIAN PERSAMAAN SCHRÖDINGER ATOM HIDROGENIK

2006 ◽  
Vol 7 (1) ◽  
pp. 11-23
Author(s):  
Paken Pandiangan ◽  
Supriyadi Supriyadi ◽  
A Arkundato
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Wave Functions ◽  
Radial Wave ◽  
Action Integral ◽  
Method Approach

The research computed the energy levels and radial wave functions of the  Hydrogen Atom. The method used for computation was FEM (finite element method). Using the variational method approach, FEM was applied to the action integral of  Schrödinger equation. This lead to the eigenvalue equation in the form of  global matrix equation. The results of computation were depended on boundary of the action integral of Schrödinger equation and number of elements. For boundary 0 - 100a0 and 100 elements,  they were the realistic and best choice of computation to the closed  analytic results. The computation of first five energy levels resulted E1 = -0.99917211 R∞, E2 = -0.24984445 R∞, E3 = -0.11105532 R∞,           E4 = -0.06247405 R∞ and  E5 = -0.03998598 R∞ where 1 R∞ = 13.6 eV. They had relative error under 0.1% to the analytic results.  

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