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 → ∞.

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.

Superconductivity in R2-zCezCuO4-Type Compounds

1998 ◽  
Vol 12 (29n31) ◽  
pp. 2965-2970 ◽  
Author(s):  
Howard A. Blackstead ◽  
John D. Dow ◽  
Martin Lehmann
Keyword(s):  
Angular Momentum ◽  
Rare Earth ◽  
Crystal Structures ◽  
Quantum Number ◽  
Weak Ferromagnetism ◽  
Rare Earth Ion ◽  
Oxide Layers ◽  
Angular Momentum Quantum Number ◽  
Natural Superlattice ◽  
P Type

The superconductivity of R 2-z Ce z CuO 4 (R214) is discussed and compared with the superconductivity of the 1 × 1 natural superlattice made of it and various oxide layers, R 2-z Ce z Sr 2 Cu 2 MO 10 (R222M10), where R is a tri-valent rare-earth ion and M=Nb, Ta, Ru, or Ti. Using simple models, we are able to understand the dependences on rare-earth size of superconductivity, of the ability to fabricate R214, of the onset of weak ferromagnetism and of the onset of crystal distortions. We can also understand the dependence of R214 superconductivity on angular momentum quantum number L and the superconductivity of Gd222Nb10 when Gd214 does not superconduct. We predict that the R214 superconductors are p-type and that the superconducting layers in R214 are not the same layers of the crystal structures as in R222Nb10.

Sign in / Sign up

Export Citation Format

Share Document