Torsional energy levels and wave functions

1992 ◽  
Vol 13 (7) ◽  
pp. 874-882 ◽  
Author(s):  
Alice Chung-Phillips
Keyword(s):  
Energy Levels ◽  
Wave Functions ◽  
Torsional Energy

scholarly journals Intercombination Transitions between Levels X1Σg+ and A 3Πu in C2

1987 ◽  
Vol 120 ◽  
pp. 103-105
Author(s):  
J. Le Bourlot ◽  
E. Roueff
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Wave Functions ◽  
Spin Orbit Coupling ◽  
Energy Matrix ◽  
First Order ◽  
Emission Transition ◽  
Intercombination Transition ◽  
The One ◽  
Potential Curves

We present a new calculation of intercombination transition probabilities between levels X1Σg+ and a 3Πu of the C2 molecule. Starting from experimental energy levels, we calculate RKR potential curves using Leroy's Near Dissociation Expansion (NDE) method; these curves give us wave functions for all levels of interest. We then compute the energy matrix for the four lowest states of C2, taking into account Spin-Orbit coupling between a 3Πu and A 1Πu on the one hand and X 1Σ+g and b 3Σg− on the other. First order wave functions are then derived by diagonalization. Einstein emission transition probabilities of the Intercombination lines are finally obtained.

Relativistic quantum bouncing particles in a homogeneous gravitational field

2021 ◽  
pp. 2150098
Author(s):  
Ar Rohim ◽  
Kazushige Ueda ◽  
Kazuhiro Yamamoto ◽  
Shih-Yuin Lin
Keyword(s):  
Gravitational Field ◽  
Relativistic Effect ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
Wave Functions ◽  
Dirac Equations ◽  
Rindler Coordinates ◽  
Klein Gordon ◽  
Homogeneous Gravitational Field

In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein–Gordon and Dirac equations in Rindler coordinates with the boundary conditions mimicking a uniformly accelerated mirror in Minkowski space. In the nonrelativistic limit, all these models in the comoving frame reduce to the familiar eigenvalue problem for the Schrödinger equation with a fixed floor in a linear gravitational potential, as expected. We find that the transition frequency between two energy levels of a bouncing Dirac particle is greater than the counterpart of a Klein–Gordon particle, while both are greater than their nonrelativistic limit. The different corrections to eigen-energies of particles of different nature are associated with the different behaviors of their wave functions around the mirror boundary.

Semi-empirical Molecular Orbital Energy Levels of the Hexammine and Chloroammine Complexes of Co(IV)

1967 ◽  
Vol 22 (2) ◽  
pp. 170-175 ◽  
Author(s):  
Walter A. Yeranos ◽  
David A. Hasman
Keyword(s):  
Molecular Orbital ◽  
Energy Levels ◽  
Empirical Evaluation ◽  
Wave Functions ◽  
Electronic Transitions ◽  
Orbital Energy ◽  
Molecular Orbital Energy ◽  
The One ◽  
Semi Empirical

Using the recently proposed reciprocal mean for the semi-empirical evaluation of resonance integrals, as well as approximate SCF wave functions for Co3+, the one-electron molecular energy levels of Co (NH3) 3+, Co (NH3) 5Cl2+, and Co (NH3) 4Cl21+ have been redetermined within the WOLFSBERG–HELMHOLZ approximation. The outcome of the study fits remarkably well with the observed electronic transitions in the u.v. spectra of these complexes and prompts different band assignments than previously suggested.

scholarly journals Spin-0 system of DKP equation in the background of a flat class of Gödel-type spacetime

2019 ◽  
Vol 35 (07) ◽  
pp. 2050031 ◽  
Author(s):  
Faizuddin Ahmed ◽  
Hassan Hassanabadi
Keyword(s):  
Energy Levels ◽  
Wave Functions ◽  
Dkp Equation ◽  
Free Particles ◽  
The Individual

In this paper, we investigate the Duffin–Kemmer–Petiau (DKP) equation for spin-0 system of charge-free particles in the background of a flat class of Gödel-type spacetimes, and evaluate the individual energy levels and corresponding wave functions in detail.

A new iterative method for calculating energy levels and wave functions

2000 ◽  
Vol 112 (20) ◽  
pp. 8765-8771 ◽  
Author(s):  
Shi-Wei Huang ◽  
Tucker Carrington
Keyword(s):  
Iterative Method ◽  
Energy Levels ◽  
Wave Functions ◽  
New Iterative Method

scholarly journals The effect of a nuclear spin on the optical spectra.—III

1930 ◽  
Vol 127 (805) ◽  
pp. 407-416 ◽  
Keyword(s):  
Interaction Energy ◽  
Nuclear Spin ◽  
Energy Levels ◽  
Optical Spectra ◽  
Wave Functions ◽  
Orbital Momentum ◽  
Multiplet Structure ◽  
Multiple Wave ◽  
First Approximation ◽  
Intensity Ratios

In two recent papers the author has discussed the effect of a nuclear spin on the optical spectra by the method of multiple wave-functions. In these papers the interaction energy of the nuclear and electron spins was not taken into account, as has been pointed out by Hill. By its omission the equations were simplified considerably, without affecting the intensity ratios of the lines of the multiplet. The problem of finding the relative intensities is a purely kinematical one, depending as it does, to the first approximation, on the un­perturbed wave-functions. In the papers cited we used the interaction energy of the nuclear spin and orbital momentum to find the 4 i n + 2 wave-functions ( i n being the number of quanta of nuclear spin) which must replace the two wave-functions necessary to describe the electron spin fine structure. In order to describe the multiple energy levels correctly we must calculate the interaction energy of the two spins in addition to the energy increments already calculated in I and II. This is the first purpose of the present paper, and the work is carried out for the cases i n = ½, 1, 1½, 4½. It is found that in the case of the p ½ levels the interaction energy of the two spins is equal to that of the nuclear spin and orbital momentum, while for the p 3/2 levels the ratio is — ⅕. It is further found that the energy levels of the S terms are correctly given in I and II. As regards comparison with Jackson’s results in the case of cæsium, it would seen that, the separation of the p -levels being very small in comparison with that of the S-level, he has been able to observe the multiplet structure of the lines due to the separation of the S-level only. If we make this assumption it will be seen on reference to I that our results agree quite well with his observations.

SPATIAL CORRELATIONS OF CHAOTIC WAVE FUNCTIONS

1996 ◽  
Vol 10 (03n05) ◽  
pp. 69-80 ◽  
Author(s):  
VLADIMIR N. PRIGODIN ◽  
NOBUHIKO TANIGUCHI
Keyword(s):  
Wave Function ◽  
Joint Distribution ◽  
Energy Levels ◽  
Density Fluctuations ◽  
Wave Functions ◽  
Spatial Correlations ◽  
Large Fluctuations ◽  
Amplitude Correlation ◽  
Universal Law ◽  
Function Density

The statistics of the spatial correlations of eigenfunctions is investigated in chaotic systems with or without time-reversal symmetry. It is rigorously shown that wave functions corresponding to different energy levels are uncorrelated in space. At a given eigenstate, we find that though the background of wave function density fluctuates strongly, there exist the long-standing Friedel oscillations in wave function intensity. The joint distribution of the intensity at two separate space points is presented by the universal law with one parameter — the average amplitude correlation. This distribution encompasses two different regions: One with an independent joint distribution for small values of density fluctuations, and the other showing an increasing spatial correlation for the large fluctuations.

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

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