Hydrogenic Wave Functions for an Extended, Uniformly Charged Nucleus

1972 ◽  
Vol 40 (7) ◽  
pp. 969-971 ◽  
Author(s):  
A. F. Yano ◽  
F. B. Yano
Keyword(s):  
Wave Functions ◽  
Charged Nucleus

Alternative form of the hydrogenic wave functions for an extended, uniformly charged nucleus

1980 ◽  
Vol 48 (11) ◽  
pp. 949-953 ◽  
Author(s):  
E. Ley‐Koo ◽  
E. Castaño ◽  
D. Finotello ◽  
E. Nahmad‐Achar ◽  
S. Ulloa
Keyword(s):  
Wave Functions ◽  
Alternative Form ◽  
Charged Nucleus

Photo-electric absorption in hydrogen-like atoms

1932 ◽  
Vol 28 (2) ◽  
pp. 209-218 ◽  
Author(s):  
P. A. M. Dirac ◽  
J. W. Harding
Keyword(s):  
Central Charge ◽  
Bound State ◽  
Incident Radiation ◽  
Wave Functions ◽  
Central Field ◽  
Electronic Interaction ◽  
Rate Of Absorption ◽  
Screening Factor ◽  
Charged Nucleus ◽  
Partial Correction

If light of a frequency which corresponds to an energy greater than the ionisation potential falls on an atom, an electron may be ejected and energy absorbed. To calculate the absorption coefficient, or the rate of absorption of energy per unit intensity of incident radiation for a given frequency, one must first choose a model for the atom. If we confine ourselves to the inner K electrons there will be two electrons in this shell for the heavier atoms, and a fairly good model of the atom is obtained by considering each electron to be moving independently in a central field of force due to the charged nucleus: i.e. we neglect electronic interaction and assume that the wave functions for the system are hydrogenic. Some writers make a partial correction for this neglect of interaction by modifying the central charge through the introduction of a screening factor which is so chosen that the minimum calculated energy required to remove one of the K electrons will agree with the experimental value provided by the K absorption edge. In general, however, the approximation is fairly good, and this is particularly so in the interior of a star where the atoms are highly ionised. It is not so good when the atom is bound as in a metal, and, of course, most of the laboratory work has been carried out on atoms in this bound state.

Magnetotunneling spectroscopy imaging of electron wave functions in self-assembled InAs quantum dots

2001 ◽  
Vol 171 (12) ◽  
pp. 1365
Author(s):  
E.E. Vdovin ◽  
Yu.N. Khanin ◽  
Yu.V. Dubrovskii ◽  
A. Veretennikov ◽  
A. Levin ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Wave Functions ◽  
Electron Wave ◽  
Inas Quantum Dots ◽  
Self Assembled

Gravity as the curvature of the wave function of the universe.

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Main Task ◽  
Reference Systems ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Principle Of Equivalence ◽  
Relative Wave Function ◽  
New Equation ◽  
The Universe

Modern general theory of relativity considers gravity as the curvature of space-time. The theory is based on the principle of equivalence. All bodies fall with the same acceleration in the gravitational field, which is equivalent to locally accelerated reference systems. In this article, we will affirm the concept of gravity as the curvature of the relative wave function of the Universe. That is, a change in the phase of the universal wave function of the Universe near a massive body leads to a change in all other wave functions of bodies. The main task is to find the form of the relative wave function of the Universe, as well as a new equation of gravity for connecting the curvature of the wave function and the density of matter.

On the conformational structure of nicotinamide and methyl-1,4-dihydronicotinamide

1979 ◽  
Vol 44 (9) ◽  
pp. 2633-2638 ◽  
Author(s):  
Hans-Jörg Hofmann ◽  
Josef Kuthan
Keyword(s):  
Molecular Structure ◽  
Continuum Model ◽  
Model Analysis ◽  
Wave Functions ◽  
Conformational Structure ◽  
Influence Of Solvent

The conformation of nicotinamide (I) and 1-methyl-1,4-dihydronicotinamide (II) was examined using the NDDO method. The influence of solvent on the molecular structure of the title compounds was estimated by means of a continuum model. Analysis of the NDDO wave functions contributes to the knowledge about the mechanism of the NADH reduction.

An ab initio MO study of conformation structure of nicotinamide and its derivatives

1983 ◽  
Vol 48 (7) ◽  
pp. 1842-1853 ◽  
Author(s):  
Stanislav Böhm ◽  
Josef Kuthan
Keyword(s):  
Ab Initio ◽  
Wave Functions ◽  
Semiempirical Calculations ◽  
Rigid Rotor ◽  
Qualitative Similarity ◽  
Ab Initio Mo ◽  
Experimental Findings

Conformation of nicotinamide (I), 3-carbamoylpyridinium (IIa), 1-methyl-3-carbamoylpyridinium (IIb), and 1-methyl-1,4-dihydronicotinamide (IIIa) has been studied in the rigid rotor approximation on the basis of non-empirical STO-3G wave functions. The rotation barriers decrease in the order: IIIa > I ~ IIb > IIa. When confronted with semiempirical calculations, the conformation curves of molecular energy show a better qualitative similarity to the EHT than to NDDO and particularly to CNDO/2 curves. Relation of the calculated characteristics to experimental findings is discussed.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

Quantum Boxes, Stringed Instruments

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Energy Level ◽  
Schrödinger Equation ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Wave Functions ◽  
Energy Level Diagram ◽  
One Dimensional ◽  
Stringed Instruments ◽  
Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

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