scholarly journals The function of the radial wave of a hydrogen atom in the principal quantum numbers (n) 4 and 5

2019 ◽  
Vol 1211 ◽  
pp. 012052
Author(s):  
B Supriadi ◽  
A Harijanto ◽  
M Maulana ◽  
Z R Ridlo ◽  
W D Wisesa ◽  
...  
Keyword(s):  
Hydrogen Atom ◽  
Radial Wave ◽  
Quantum Numbers

scholarly journals The bound state solutions of the D-dimensional Schrödinger equation for the Woods–Saxon potential

2016 ◽  
Vol 25 (01) ◽  
pp. 1650002 ◽  
Author(s):  
V. H. Badalov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Wave Functions ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Pekeris Approximation

In this work, the analytical solutions of the [Formula: see text]-dimensional radial Schrödinger equation are studied in great detail for the Wood–Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the Nikiforov–Uvarov (NU) and Supersymmetric quantum mechanics (SUSYQM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformed each other is demonstrated. In addition, a finite number energy spectrum depending on the depth of the potential [Formula: see text], the radial [Formula: see text] and orbital [Formula: see text] quantum numbers and parameters [Formula: see text] are defined as well.

Structure of the Atom

2021 ◽  
pp. 64-80
Author(s):  
Christopher O. Oriakhi
Keyword(s):  
Hydrogen Atom ◽  
Mechanical Model ◽  
Atomic Orbital ◽  
Energy Levels ◽  
Quantum Mechanical ◽  
Electron Configuration ◽  
Fundamental Nature ◽  
Quantum Mechanical Model ◽  
Quantum Numbers

Structure of the Atom describes the quantum-mechanical model of the atom, which explains the fundamental nature of energy and matter, in terms of how electrons are arranged within atoms and how that arrangement determines the ultimate chemical and physical properties of elements. A discussion of atomic spectra, the Bohr model of the hydrogen atom, and the quantum numbers of an atomic orbital is provided. Other topics include the determination of quantum numbers from energy levels, the shapes of atomic orbitals, electron filling order, and the determination of the complete electron configuration of the elements.

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.  

Schrödinger’s Derivation of the Wave Equation

2020 ◽  
pp. 89-110
Author(s):  
Jim Baggott
Keyword(s):  
Wave Equation ◽  
Hydrogen Atom ◽  
Wave Motion ◽  
Classical Equation ◽  
Erwin Schrödinger ◽  
Quantum Numbers ◽  
Vibrating String ◽  
Spectroscopy Studies ◽  
Phd Thesis ◽  
Natural Way

Bohr’s theory of the atom was in trouble as soon as it was formulated. Further detailed spectroscopy studies encouraged a proliferation of quantum numbers and ‘selection rules’ in what became known as the Bohr–Sommerfeld model. It couldn’t last, and by 1925 the theory was in crisis. The immediate concern was with the quantum numbers themselves. Where did they come from? Could de Broglie’s hypothesis shed any light? In October 1925 the attentions of Erwin Schrödinger were drawn to a footnote in one of Einstein’s recent papers. Intrigued, Schrödinger acquired a copy of de Broglie’s PhD thesis. Although he eventually published a more obscure derivation, Schrödinger essentially applied the de Broglie relation to the classical equation of wave motion. He applied the result to the hydrogen atom, and showed that the quantum numbers emerge ‘in the same natural way as the integers specifying the number of nodes in a vibrating string’.

The Hydrogen Atom and Its Colorful Photons

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Hydrogen Atom ◽  
Excited States ◽  
Probability Distributions ◽  
Wave Functions ◽  
Visible Range ◽  
Fixed Position ◽  
Balmer Series ◽  
Classical Physics ◽  
Quantum Numbers ◽  
Higher Excited States

The energies, kets and wave functions obtained from the Schrödinger equation for the hydrogen atom are examined in Chapter 9. Three quantum numbers are identified. The energies turn out to be the same as in the Bohr model, and an energy-level diagram appropriate to the quantum description is constructed. Graphs of the probability distributions are interpreted as the electron being in a “cloud” around the proton, rather than at a fixed position: the atom is fuzzy, not sharp-edged. The wavelengths of the five photons of the Balmer series are shown to be in the visible range. These photons are emitted when electrons transition from higher-excited states to the second lowest one, which means that electronic-type transitions underlie the presence of colors in our visible environment. The non-collapse of the atom, required by classical physics, is shown to arise from the structure of Schrödinger’s equation.

The hydrogen atom and the periodic table

2018 ◽  
Author(s):  
L. Solymar ◽  
D. Walsh ◽  
R. R. A. Syms
Keyword(s):  
Hydrogen Atom ◽  
Periodic Table ◽  
Energy Levels ◽  
Simple Approach ◽  
Wave Functions ◽  
Exclusion Principle ◽  
Negative Particle ◽  
Quantum Numbers ◽  
Positive Particle

Investigates the energy levels in a configuration when a heavy positive particle (proton) and a light negative particle (electron) are present. The wave functions and permissible energy levels are derived from Schrödinger's equation. The role of quantum numbers is discussed. Electron spin and Pauli’s exclusion principle are introduced. The properties of the elements in the periodic table are discussed, based on the properties of the hydrogen atom. Exceptions when such a simple approach does not work are further discussed.

scholarly journals Solution of spherical equation in 3 dimensions for hydrogen atom with quantum numbers 4≤ n≤ 5

2019 ◽  
Vol 1211 ◽  
pp. 012054
Author(s):  
B Supriadi ◽  
Z R Ridlo ◽  
F Fuadah ◽  
M A Halim ◽  
M Maulana ◽  
...  
Keyword(s):  
Hydrogen Atom ◽  
Quantum Numbers

MULTIPOLE MATRIX ELEMENTS FOR DH-SYSTEMS AND THEIR ASYMPTOTICS

1995 ◽  
Vol 09 (20) ◽  
pp. 2699-2718 ◽  
Author(s):  
V.F. TARASOV
Keyword(s):  
Hydrogen Atom ◽  
Singular Point ◽  
Diagonal Matrix ◽  
New Method ◽  
Matrix Elements ◽  
Exact Asymptotics ◽  
Radial Functions ◽  
Quantum Numbers ◽  
Analytical Expressions ◽  
Math Phys

A “DH-system” is defined as a multidimensional hydrogen atom (or its one-particle analogue), D≥1. Investigating many Coulomb problems in ℝD it is necessary to know exact analytical expressions of multipole matrix elements <q|rk|q'>D for DH-systems, where q=(N, µ) is a set of parameters, N —"principal” and µ — "orbital” quantum numbers. The paper deals with the new method for the evaluation of similar matrix elements using new properties of Appell’s function F2(x, y) to the vicinity of the singular point (1, 1). Such approach allows: 1) to get exact analytical expressions of these matrix elements (considering the selection rules) by means of Appell’s F2 (or Clausen’s 3F2) functions; 2) to reveal “latent” symmetry of diagonal matrix elements with respect to the point k0=−3/2, the above symmetry is connected with the property of Appell’s function F2 (1,1) mirror-like symmetry; 3) to find (exact) asymptotics of the off-diagonal matrix elements in terms of Horn’s function ψ1 (x, y); 4) to prove that the orthogonality of radial functions fNµ (D, r) over N and μ for DH-systems is connected with the properties of Appell’s F2 function to the vicinity of the singular point (1, 1), it generalizes the known result for 3H-atom by Pasternack and Sternheimer, J. Math. Phys.3, 1280 (1962).

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