Spheroidal Coordinates and Wave Functions

2002 ◽  
pp. 13-60 ◽  
Keyword(s):  
Wave Functions ◽  
Spheroidal Coordinates

Self-consistent field for molecular hydrogen

1938 ◽  
Vol 34 (2) ◽  
pp. 204-212 ◽  
Author(s):  
C. A. Coulson
Keyword(s):  
Ground State ◽  
Hydrogen Molecule ◽  
Wave Functions ◽  
Complex Molecules ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Analytical Expansion ◽  
Spheroidal Coordinates ◽  
Accurate Wave

The method of the self-consistent field is applied to a discussion of the energy and wave-functions of the ground state of the hydrogen molecule; an analytical expansion of the wave-function is given in terms of spheroidal coordinates, and the distribution of charge is determined. Two simpler, though less accurate, wave-functions for the molecule are also included, and the possibility of using the method for more complex molecules is discussed.

The Two Centre Dirac Equation

1976 ◽  
Vol 31 (1) ◽  
pp. 1-30 ◽  
Author(s):  
Berndt Müller ◽  
Walter Greiner
Keyword(s):  
Dirac Equation ◽  
Heavy Ions ◽  
Nuclear Charge ◽  
Basis Functions ◽  
Wave Functions ◽  
Matrix Elements ◽  
Prolate Spheroidal ◽  
Prolate Spheroidal Coordinates ◽  
Spheroidal Coordinates ◽  
Dirac Hamiltonian

During collisions of heavy ions with heavy targets below the Coulomb barrier, adiabatic molecular orbitals are formed for the inner electrons. Deviations from adiabaticity lead to coupling between various states and can be treated by time-dependent perturbation theory. For high charges ( Z1+Z2 ≧ 60) the molecular electrons are highly relativistic. Therefore, the Dirac equation has to be used to obtain the energies and wave functions. The Dirac Hamiltonian is transformed into the intrinsic rotating coordinate system where prolate spheroidal coordinates are introduced. A set of basis functions is proposed which allows the evaluation of all matrix elements of the Dirac Hamiltonian analytically. The resulting matrix is diagonalized numerically. The finite nuclear charge distribution is also taken into account. Results are presented and discussed for various characteristic systems, e. g. Br-Br, Ni-Ni, I-I, Br-Zr, I-Au, U -U, etc.

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.

Sign in / Sign up

Export Citation Format

Share Document