Positrons vs electrons channeling in silicon crystal: energy levels, wave functions and quantum chaos manifestations

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.

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Quantum chaos and statistical properties of energy levels for atom in parallel electric and magnetic fields

Modern Physics Letters B ◽

10.1142/s0217984915502486 ◽

2015 ◽

Vol 29 (35n36) ◽

pp. 1550248

Author(s):

Hai-Feng Yang ◽

Yong-Gang Tan ◽

Zhong-Li Liu ◽

Hong-Zhi Fu

Keyword(s):

Magnetic Fields ◽

Quantum Chaos ◽

Chaotic Dynamics ◽

Nearest Neighbor ◽

Energy Levels ◽

Statistical Properties ◽

The Core ◽

Ideal System ◽

Electric And Magnetic Fields ◽

Diagonalization Method

In this paper, the statistical properties of energy levels are studied numerically for atom in parallel electric and magnetic fields, which is an ideal system to examine the contributions of external fields and ionic core to quantum chaos. The Stark maps of diamagnetic spectra and nearest neighbor spacing (NNS) distributions are obtained by diagonalization method incorporating core effect. We identify obvious level anti-crossing and large value of [Formula: see text] for barium, indicating that core effect has predominant contribution to chaotic dynamics in barium. To study the core effect in detail, we sweep the quantum defect artificially and find that larger core effect will undoubtedly induce stronger chaotic dynamics.

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Relativistic quantum bouncing particles in a homogeneous gravitational field

International Journal of Modern Physics D ◽

10.1142/s021827182150098x ◽

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.

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

Zeitschrift für Naturforschung A ◽

10.1515/zna-1967-0206 ◽

1967 ◽

Vol 22 (2) ◽

pp. 170-175 ◽

Cited By ~ 5

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.

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

Modern Physics Letters A ◽

10.1142/s0217732320500315 ◽

2019 ◽

Vol 35 (07) ◽

pp. 2050031 ◽

Cited By ~ 4

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.

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A new iterative method for calculating energy levels and wave functions

The Journal of Chemical Physics ◽

10.1063/1.481492 ◽

2000 ◽

Vol 112 (20) ◽

pp. 8765-8771 ◽

Cited By ~ 76

Author(s):

Shi-Wei Huang ◽

Tucker Carrington

Keyword(s):

Iterative Method ◽

Energy Levels ◽

Wave Functions ◽

New Iterative Method

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Influence of Substrate Type and Dose of Implanted Ions on the Electrical Parameters of Silicon in Terms of Improving the Efficiency of Photovoltaic Cells

Energies ◽

10.3390/en13246708 ◽

2020 ◽

Vol 13 (24) ◽

pp. 6708

Author(s):

Paweł Węgierek ◽

Justyna Pastuszak ◽

Kamil Dziadosz ◽

Marcin Turek

Keyword(s):

Electrical Properties ◽

Energy Gap ◽

Energy Levels ◽

Silicon Crystal ◽

Photovoltaic Cells ◽

Photovoltaic Cell ◽

Additional Energy ◽

Influence Of Substrate ◽

Substrate Doping ◽

Different Doses

The main goal of this work was to conduct a comparative analysis of the electrical properties of the silicon implanted with neon ions, depending on the dose of ions and the type of substrate doping, for the possibility of generating additional energy levels by ion implantation in terms of improving the efficiency of photovoltaic cells made on its basis. The article presents the results of research on the capacitance and conductance of silicon samples doped with boron and phosphorus, the structure of which was modified in the implantation process with Ne+ ions with energy E = 100 keV and different doses. The analysis of changes in electrical properties recorded at the annealing temperature of the samples Ta = 298 K, 473 K, 598 K, 673 K, and 873 K, concerned the influence of the test temperature in the range from 203 K to 373 K, as well as the frequency f from 100 Hz to 10 MHz, and voltage U from 0.25 V to 2 V. It was possible to detect intermediate bands in the tested samples and determine their position in the band gap by estimating the activation energy value. By means of implantation, it is possible to modify the width of the silicon energy gap, the value of which directly affects the efficiency of the photovoltaic cell made on its basis. By introducing appropriate defects into the silicon crystal lattice, contributing to a change in the value of the energy gap Eg, it is possible to increase the efficiency of the solar cell. On the basis of the obtained results, it can be seen that the highest activation energies are achieved for samples doped with phosphorus.

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

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1930.0067 ◽

1930 ◽

Vol 127 (805) ◽

pp. 407-416 ◽

Cited By ~ 3

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.

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SPATIAL CORRELATIONS OF CHAOTIC WAVE FUNCTIONS

Modern Physics Letters B ◽

10.1142/s0217984996000110 ◽

1996 ◽

Vol 10 (03n05) ◽

pp. 69-80 ◽

Cited By ~ 8

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.

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