Bond strength and bond angles for hybrid orbitals composed of arbitrary sets of orbital angular momentum quantum number

1987 ◽  
Vol 32 (1) ◽  
pp. 13-18 ◽  
Author(s):  
Chang-Guo Zhan ◽  
Frank Liu (Liu Fan) ◽  
Zhen-Min Hu
Keyword(s):  
Angular Momentum ◽  
Bond Strength ◽  
Quantum Number ◽  
Orbital Angular Momentum ◽  
Bond Angles ◽  
Angular Momentum Quantum Number ◽  
Hybrid Orbitals

The linear potential eigenenergy equation. I: the coefficients Kn(3l′)

1979 ◽  
Vol 57 (3) ◽  
pp. 417-427 ◽  
Author(s):  
Adel F. Antippa ◽  
Toan Nguyen Ky
Keyword(s):  
Angular Momentum ◽  
Quantum Number ◽  
Asymptotic Limit ◽  
Linear Potential ◽  
Angular Momentum Quantum Number ◽  
Explicit Expressions

We derive explicit expressions for the coefficients Kn(l) of the linear potential eigenenergy equation for values of the angular momentum quantum number given by l = 3l′. The coefficients Kn(3l′) are obtained by taking the asymptotic limit of the previously derived functions Kn3k+1(3l′), as k → ∞.

STEREO PHOTOGRAPHY OF ATOMIC ARRANGEMENT AND ATOMIC-ORBITAL ANALYSIS BY TWO-DIMENSIONAL PHOTOELECTRON SPECTROSCOPY

2007 ◽  
Vol 14 (04) ◽  
pp. 637-643 ◽  
Author(s):  
FUMIHIKO MATSUI ◽  
TOMOHIRO MATSUSHITA ◽  
FANG ZHUN GUO ◽  
HIROSHI DAIMON
Keyword(s):  
Angular Momentum ◽  
Valence Band ◽  
Orbital Angular Momentum ◽  
Photoelectron Spectroscopy ◽  
Atomic Orbital ◽  
Incident Light ◽  
Atomic Orbitals ◽  
Angular Momentum Quantum Number ◽  
The Difference ◽  
Orbital Analysis

The circular dichroism of photoelectron forward focusing peak rotation around the incident-light axis reflects the orbital angular momentum of the excited core level and is inversely proportional to the distance between the emitter and scatterer atoms. This is the basis for the stereo photograph of the atomic arrangements. These rotations are also found in the case of the valence band excitation. The rotation for the 2pxy band of graphite was about twice those from 2s and 2pz bands, corresponding to the difference in the orbital angular momentum quantum number of each band. Simultaneously, photoelectron intensity from the bottom of the 2s band was observed at the Γ point of every other Brillouin zone reflecting the photoelectron structure factor that corresponds to the interference of photoelectron waves from 2s atomic orbitals within a unit cell. The origin of the dual behavior that appeared in the observation of a local angular momentum from a delocalized valence band is discussed.

THE KLEIN–GORDON EQUATION WITH A COULOMB PLUS SCALAR POTENTIAL IN D DIMENSIONS

2004 ◽  
Vol 13 (03) ◽  
pp. 597-610 ◽  
Author(s):  
ZHONG-QI MA ◽  
SHI-HAI DONG ◽  
XIAO-YAN GU ◽  
JIANG YU ◽  
M. LOZADA-CASSOU
Keyword(s):  
Angular Momentum ◽  
Quantum Number ◽  
Coulomb Potential ◽  
Gordon Equation ◽  
Scalar Potential ◽  
Positive Energy ◽  
Angular Momentum Quantum Number ◽  
Klein Gordon ◽  
Klein Gordon Equation

The solutions of the Klein–Gordon equation with a Coulomb plus scalar potential in D dimensions are exactly obtained. The energy E(n,l,D) is analytically presented and the dependence of the energy E(n,l,D) on the dimension D is analyzed in some detail. The positive energy E(n,0,D) first decreases and then increases with increasing dimension D. The positive energy E(n,l D)(l≠0) increases with increasing dimension D. The dependences of the negative energies E(n,0,D) and E(n,l,D)(l≠0) on the dimension D are opposite to those of the corresponding positive energies E(n,0,D) and E(n,l,D)(l≠0). It is found that the energy E(n,0,D) is symmetric with respect to D=2 for D∈(0,4). It is also found that the energy E(n,l,D)(l≠0) is almost independent of the angular momentum quantum number l for large D and is completely independent of the angular momentum quantum number l if the Coulomb potential is equal to the scalar one. The energy E(n,l D) is almost overlapping for large D.

The effect of anisotropy in the modified Jiles-Atherton model of static hysteresis

2011 ◽  
Vol 60 (1) ◽  
pp. 49-57 ◽  
Author(s):  
Krzysztof Chwastek ◽  
Jan Szczygłowski
Keyword(s):  
Angular Momentum ◽  
Quantum Number ◽  
Angular Momentum Quantum Number ◽  
Brillouin Function ◽  
Anhysteretic Magnetization

The effect of anisotropy in the modified Jiles-Atherton model of static hysteresisAn extension of the modified Jiles-Atherton description to include the effect of anisotropy is presented. Anisotropy is related to the value of the angular momentum quantum numberJ, which affects the form of the Brillouin function used to describe the anhysteretic magnetization. Moreover the shape of magnetization dependentR(m)function is influenced by the choice of theJvalue.

scholarly journals Scattering of charged fermion to two-dimensional wormhole with constant axial magnetic flux

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Kulapant Pimsamarn ◽  
Piyabut Burikham ◽  
Trithos Rojjanason
Keyword(s):  
Angular Momentum ◽  
Magnetic Flux ◽  
Quantum Number ◽  
Normal Modes ◽  
Quasinormal Modes ◽  
Unitarity Condition ◽  
Charged Fermion ◽  
Angular Momentum Quantum Number ◽  
Transmitted Waves ◽  
Generic Relation

AbstractScattering of charged fermion with $$(1+2)$$ ( 1 + 2 ) -dimensional wormhole in the presence of constant axial magnetic flux is explored. By extending the class of fermionic solutions of the Dirac equation in the curved space of wormhole surface to include normal modes with real energy and momentum, we found a quantum selection rule for the scattering of fermion waves to the wormhole. The newly found momentum–angular momentum relation implies that only fermion with the quantized momentum $$k=m'/a\sqrt{q}$$ k = m ′ / a q can be transmitted through the hole. The allowed momentum is proportional to an effective angular momentum quantum number $$m'$$ m ′ and inversely proportional to the radius of the throat of the wormhole a. Flux dependence of the effective angular momentum quantum number permits us to select fermions that can pass through according to their momenta. A conservation law is also naturally enforced in terms of the unitarity condition among the incident, reflected, and transmitted waves. The scattering involving quasinormal modes (QNMs) of fermionic states in the wormhole is subsequently explored. It is found that the transmitted waves through the wormhole for all scenarios involving QNMs are mostly suppressed and decaying in time. In the case of QNMs scattering, the unitarity condition is violated but a more generic relation of the scattering coefficients is established. When the magnetic flux $$\phi =mhc/e$$ ϕ = m h c / e , i.e., quantized in units of the magnetic flux quantum hc/e, the fermion will tunnel through the wormhole with zero reflection.

SOME DIRECTIONAL CORRELATION FUNCTIONS FOR SUCCESSIVE NUCLEAR RADIATIONS

1952 ◽  
Vol 30 (2) ◽  
pp. 130-146 ◽  
Author(s):  
F. G. Hess
Keyword(s):  
Correlation Function ◽  
Angular Momentum ◽  
Quantum Number ◽  
Correlation Functions ◽  
The Other ◽  
Gamma Correlation ◽  
Angular Momentum Quantum Number ◽  
Directional Correlation Function

A method of evaluating the sums of angular momentum coefficients appearing in the directional correlation function for successive nuclear radiations is presented. The sums are evaluated for the simplest cases and alpha–gamma and gamma–gamma correlation functions are calculated for these cases—the angular momentum quantum number of one of the emitted particles being arbitrary and that of the other being 1 or 2.

scholarly journals Electron cyclotron motion excited surface plasmon and radiation with orbital angular momentum on a semiconductor thin film

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Yung-Chiang Lan ◽  
Chia-Hui Shen ◽  
Chih-Min Chen
Keyword(s):  
Thin Film ◽  
Angular Momentum ◽  
Quantum Number ◽  
Electron Energy ◽  
Orbital Angular Momentum ◽  
Fixed Number ◽  
Electron Cyclotron ◽  
Flat Band ◽  
Cyclotron Motion ◽  
Particle In Cell

Abstract In this work, surface plasmons (SPs) on a germanium (Ge) thin film in terahertz (THz) region that are excited by electron cyclotron motion (ECM) and the subsequent SP emission (SPE) by adding Ge gratings on the film are explored by finite-difference time-domain (FDTD) and particle-in-cell FDTD (PIC-FDTD) simulations. The optical properties of ECM-excited SPs are the same as those of SPs that are excited by electron straight motion (ESM). For operating at the flat band of SPs’ dispersion curve on the Ge film, changing the electron energy will only change the wavevector of SPs and hence the number of periods of SPs on the circular orbital. When the periodic gratings are deposited on the Ge film along the circular orbital of electrons, the emitted SPE contains the orbital angular momentum (OAM). The number of arms and chirality of the spiral patterns in phase map (i.e. the quantum number of OAM) of SPE are determined by the difference between the number of SPs’ periods and the number of gratings. Manipulations of the quantum number of OAM by changing the number of gratings for a fixed electron energy and by changing the electron energy for a fixed number of gratings are also demonstrated. This work provides an active OAM source and it is not required to launch circularly polarized beams or pumping beams into the structure.

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