The evolution and revival structure of angular momentum quantum wave packets

1999 ◽  
Vol 77 (7) ◽  
pp. 491-503 ◽  
Author(s):  
Marcis Auzinsh
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Wave Packet ◽  
Electric Field ◽  
Stark Effect ◽  
Wave Packets ◽  
Zeeman Effect ◽  
Permanent Magnetic Field ◽  
Stark Effects ◽  
Quadratic Stark Effect

In this paper, a coherent superposition of angular-momentum states created by absorption of polarized light by molecules is analyzed. Attention is paid to the time evolution of wave packets representing the spatial orientation of the internuclear axis of a diatomic molecule. Two examples are considered in detail. Molecules absorbing light in a permanent magnetic field experiencing the Zeeman effect and molecules absorbing light in a permanent electric field experiencing the quadratic Stark effect. In a magnetic field, we have a wave packet that evolves in time exactly as a classical dipole oscillator in a permanent magnetic field (classical-physics picture of the Zeeman effect). In the second case, we have a wave packet that goes through periodical changes of shape of the packet with revivals of the initial shape. This is pure quantum behavior. The classical motion of angular momentum in an electric field in the case of a quadratic Stark effect is known to be a periodic. Solutions obtained for wave packet evolution are briefly compared with Rydberg-state coherent wave packets and harmonic-oscillator wave packets. Zeeman and Stark effects in small molecules continuously attract the attention of researchers, theoreticians, as well as experimentalists. These investigations allow us to obtain a deeper understanding of the interaction of molecules with stationary external fields and also can be used as a practical tool to measure different molecular characteristics, such as permanent electric or magnetic dipole moments, intramolecular perturbations, etc. It is worthwhile analyzing these effects as an evolution of wave packets. All this motivates a comparison of the quantum and classical picture of Zeeman and Stark effects in molecules.PACS No.: 33.55.Be

STUDY OF ZITTERBEWEGUNG AND THE RADIATED FIELDS IN GRAPHENE SYSTEM

2012 ◽  
Vol 26 (21) ◽  
pp. 1250139 ◽  
Author(s):  
YI-XIANG WANG ◽  
YUE-JUAN HE ◽  
SHI-JIE XIONG
Keyword(s):  
Magnetic Field ◽  
Wave Packet ◽  
Electric Field ◽  
Electric Fields ◽  
Fourier Spectrum ◽  
Dipole Moments ◽  
Wave Packets ◽  
Perpendicular Magnetic Field ◽  
Initial State

We theoretically study Zitterbewegung behavior of electrons in graphene system when the external perpendicular magnetic field exists. The initial state is assumed as a wave packet shape which is the superposition of the positive and negative LLs. The evolution of the dipole moments and the excited electric fields are calculated for the localized and extended wave packets which exhibit different behavior. We further analyze their Fourier spectrum and study which factors affect the excited electric field as it can be directly detected in experiment. The results are analyzed and discussed.

Hyperfeinstruktur, Stark-Effekt und Lebensdauern in den angeregten 5d6s6p y2D3/2,5/2 -Zuständen des Lanthan I-Spektrums/ Hyperfine Structure, Stark-Effect and Lifetimes of the Excited 5d6s6p y 2D3/2,5/2-States of the Lanthanum I Spectrum

1970 ◽  
Vol 25 (11) ◽  
pp. 1537-1545 ◽  
Author(s):  
A. Hese ◽  
G. Büldt
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Hyperfine Interaction ◽  
Detailed Analysis ◽  
Hyperfine Structure ◽  
Stark Effect ◽  
Homogeneous Electric Field ◽  
Intermediate Coupling ◽  
Quadratic Stark Effect ◽  
Measured Change

The levelcrossing method has been used for an investigation of the hyperfine structure and lifetimes in the excited 5d6s6p y 2D3/2, 5/2-states of Lanthanum I. From a detailed analysis of the measured change in intensity of the resonance light the following hyperfine interaction constants and lifetimes were deduced:Applying an additional homogeneous electric field parallel to the usual magnetic field the constants β of the quadratic Stark effect in the y 2D-states were derived from the observed shifts of the levelcrossing signals:The experimental results are interpreted theoretically by the concept of intermediate coupling using appropriate eigenvectors. The observed lifetimes and the β-values are compared with the Bates and Damgaard approximation.

Ein Level-Crossing-Experiment im angeregten (5p1/2 5d5/2)J=2-Term des Sn I zur Untersuchung der Energieverschiebungen im elektrischen Feld / Level-Crossing Experiment in the Excited (5p1/25d5/2)J=2-State of the Sn I for the Investigation of the Energy Shifts in an Electric Field

1970 ◽  
Vol 25 (5) ◽  
pp. 608-611
Author(s):  
P. Zimmermann
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Stark Effect ◽  
Second Order ◽  
Wave Functions ◽  
Zero Field ◽  
Homogeneous Electric Field ◽  
Level Crossing ◽  
Crossing Experiment ◽  
The Magnetic Field

Observing the change of the Hanle effect under the influence of a homogeneous electric field E the Stark effect of the (5p1/25d5/2)j=2-state in Sn I was studied. Due to the tensorial part β Jz2E2 in the Hamiltonian of the second order Stark effect the signal of the zero field crossing (M ∓ 2, M′ = 0 β ≷ 0 ) is shifted to the magnetic field H with gJμBH=2 | β | E2. From these shifts for different electric field strengths the value of the Stark parameter|β| = 0.21(2) MHz/(kV/cm)2 · gJ/1.13was deduced. A theoretical value of ß using Coulomb wave functions is discussed.

scholarly journals FRB coherent emission from decay of Alfvén waves

2020 ◽  
Vol 494 (2) ◽  
pp. 2385-2395 ◽  
Author(s):  
Pawan Kumar ◽  
Željka Bošnjak
Keyword(s):  
Magnetic Field ◽  
Wave Packet ◽  
Electric Field ◽  
Static Magnetic Field ◽  
Strong Electric Field ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Radio Waves ◽  
Electron Positron

ABSTRACT We present a model for fast radio bursts (FRBs) where a large-amplitude Alfvén wave packet is launched by a disturbance near the surface of a magnetar, and a substantial fraction of the wave energy is converted to coherent radio waves at a distance of a few tens of neutron star radii. The wave amplitude at the magnetar surface should be about 1011 G in order to produce an FRB of isotropic luminosity 1044 erg s−1. An electric current along the static magnetic field is required by Alfvén waves with non-zero component of transverse wave vector. The current is supplied by counter-streaming electron–positron pairs, which have to move at nearly the speed of light at larger radii as the plasma density decreases with distance from the magnetar surface. The counter-streaming pairs are subject to two-stream instability, which leads to formation of particle bunches of size of the order of c/ωp, where ωp is the plasma frequency. A strong electric field develops along the static magnetic field when the wave packet arrives at a radius where electron–positron density is insufficient to supply the current required by the wave. The electric field accelerates particle bunches along the curved magnetic field lines, and that produces the coherent FRB radiation. We provide a number of predictions of this model.

A NEWTONIAN INTERPRETATION OF THE PARAMETER “a” ASSOCIATED WITH THE KERR METRIC

1996 ◽  
Vol 11 (18) ◽  
pp. 1445-1451
Author(s):  
SUJAN SENGUPTA
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Electric Field ◽  
Unit Mass ◽  
Kerr Metric ◽  
Massive Object ◽  
Dipole Magnetic Field ◽  
Newtonian Case

The parameter “a” associated with the Kerr metric has been used to determine the rotationally induced quadrapole electric field outside a rotating massive object with external dipole magnetic field. A comparison of the result with that of the Newtonian case implies that the parameter “a” represents the angular momentum per unit mass of a rotating hollow object.

The hyperfine structure Stark effect - III. The 2 P ½ level of aluminium

1974 ◽  
Vol 338 (1612) ◽  
pp. 95-100 ◽  
Keyword(s):  
Electric Field ◽  
Frequency Shift ◽  
Hyperfine Structure ◽  
Stark Effect ◽  
Ground Level ◽  
Tensor Polarizability ◽  
Atomic Beams ◽  
Quadratic Stark Effect ◽  
Stark Operator

The quadratic Stark effect in the hyperfine structure of the 2 P ½ ground level of aluminium has been investigated by the method of atomic beams. A frequency shift caused by the application of an electric field has been interpreted in terms of an effective Stark operator, and the associated tensor polarizability α ten ( J = ½, F = 3) has a measured value of (8.13±0.72) × 10 –4 a 3 0 . The case of J = ½ is a special one in that the theoretical value of α ten ( J = ½, F = 3) vanishes in the absence of hyperfine structure effects. The inclusion of the hyperfine structure operator in a calculation of the tensor polarizability has led to a small theoretical value in agreement with experiment.

Molekülstrahl-Resonanz-Messungen von Hyperfeinstruktur, Zeeman-und Stark-Effekt an TlCl-Isotopen in verschiedenen Schwingungszuständen / Molecular Beam Resonance Measurements of Hyperfine Structure, Zeeman- and Stark-Effect of TICl-lsotopes in Different Vibrational States

1972 ◽  
Vol 27 (1) ◽  
pp. 77-91 ◽  
Author(s):  
R. Ley ◽  
W. Schauer
Keyword(s):  
Magnetic Field ◽  
Dipole Moment ◽  
Hyperfine Structure ◽  
Electric Dipole Moment ◽  
Electric Dipole ◽  
Molecular Beam ◽  
Stark Effect ◽  
Zeeman Effect ◽  
Magnetic Shielding ◽  
Vibrational States

AbstractHyperfine structure, Stark effect and Zeeman effect of the TlCl molecule have been measured with a molecular beam apparatus using electric four poles as deflecting fields and a homogeneous electric field parallel to a superimposed magnetic field in the transition region. Electric dipole transitions were induced between the hyperfine structure levels of the first rotational state J = 1 in both strong and weak external field.The following quantities could be evaluated from the spectra: the electric dipole moment µel and the magnetic rotational dipole moment µJ of the molecule, the nuclear spin-rotational interactions c1 and c2, the scalar and tensor part of the nuclear dipole-dipole interaction dS and dT, the quadrupole coupling constant e q Q of the Cl nucleus, the anisotropy of the magnetic susceptibility ξ⊥− ξ∥ , the anisotropy of the magnetic shielding of the external magnetic field at the position of both nuclei (σ⊥- σ∥)1 and (σ⊥- σ∥)2, the magnetic moment of the Cl nucleus multiplied by the scalar part of the magnetic shielding tensor µ2 · (1 - σS)2. For the most abundant isotop 205Tl35Cl the vibrational dependence of most of these quantities was measured in the vibrational states v =0, 1, 2, 3. Isotopic effects for 203Tl35Cl, 205Tl37Cl and 203Tl37Cl were investigated in the ground vibrational state. In addition the vibrational dependence of the electric dipole moment was measured for all isotopic species.It is pointed out that the usual connections between (σ⊥- σ∥)1,2 and c1,2 and between ξ⊥− ξ∥ and µJ do not hold when the excited electronic states of the molecule obey Hund’s coupling case c, which occurs most probably in TlCl.

scholarly journals Effect of combined electric and magnetic fields on the helium spectrum

1929 ◽  
Vol 122 (790) ◽  
pp. 599-603 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electric Field ◽  
Classical Theory ◽  
Stark Effect ◽  
Classical View ◽  
Electric And Magnetic Fields ◽  
Perpendicular Component ◽  
The Individual ◽  
The Magnetic Field

This paper deals with the observed effect of simultaneous electric and magnetic fields on certain of the more intense helium lines, and is further limited to the case where the fields are uniform and parallel. The effect of parallel fields was first considered by Garbasso, who adopted the classical view of the “rough” Stark-effect on H β as given by Voigt, and concluded that the effects due to the two fields should be simply superimposed. Shortly after this he was able to make visual observations which were restricted to H α owing to intensity requirements. A source of the Lo Surdo type was placed along the axis of the hollow poles of a Weiss magnet, and the analysis made with a Michelson echelon. In the electric field alone Garbasso observed two parallel components and one undisplaced perpendicular component. This corresponds to a so-called “rough” analysis of the Stark-effect in which the individual components are not observed. In the magnetic field he found a normal Zeeman pattern. With combined parallel fields there appeared two parallel components in the position of the Stark components of like polarisation, and two symmetrically placed perpendicular components with the normal Zeeman separation. This simple result could not be given a satisfactory interpretation on classical theory.

The hyperfine structure Stark effect I. Theory

1968 ◽  
Vol 305 (1480) ◽  
pp. 125-138 ◽  
Keyword(s):  
Perturbation Theory ◽  
Electric Field ◽  
Hyperfine Structure ◽  
Stark Effect ◽  
Free Atom ◽  
Uniform Electric Field ◽  
Theory Approach ◽  
Tensor Form ◽  
Quadratic Stark Effect ◽  
Effective Operators

A theory of the quadratic Stark effect is presented. It is aimed at a description of the hyperfine structure of a free atom in a uniform electric field. A perturbation theory approach is adopted and extensive use is made of effective operators. In spherical tensor form these can be written as the sum of a scalar and a tensor of rank two. Associated scalar and tensor polarizabilities are defined and their properties are discussed. A variety of applications of the theory are given.

scholarly journals WIND observations of coherent electrostatic waves in the solar wind

1999 ◽  
Vol 17 (3) ◽  
pp. 307-320 ◽  
Author(s):  
A. Mangeney ◽  
C. Salem ◽  
C. Lacombe ◽  
J.-L. Bougeret ◽  
C. Perche ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Electric Field ◽  
Plasma Frequency ◽  
Wave Packets ◽  
Double Layers ◽  
Coherent Wave ◽  
Interplanetary Physics ◽  
Ion Acoustic ◽  
Wave Forms

Abstract. The time domain sampler (TDS) experiment on WIND measures electric and magnetic wave forms with a sampling rate which reaches 120 000 points per second. We analyse here observations made in the solar wind near the Lagrange point L1. In the range of frequencies above the proton plasma frequency fpi and smaller than or of the order of the electron plasma frequency fpe, TDS observed three kinds of electrostatic (e.s.) waves: coherent wave packets of Langmuir waves with frequencies f ~ fpe, coherent wave packets with frequencies in the ion acoustic range fpi < f < fpe, and more or less isolated non-sinusoidal spikes lasting less than 1 ms. We confirm that the observed frequency of the low frequency (LF) ion acoustic wave packets is dominated by the Doppler effect: the wavelengths are short, 10 to 50 electron Debye lengths λD. The electric field in the isolated electrostatic structures (IES) and in the LF wave packets is more or less aligned with the solar wind magnetic field. Across the IES, which have a spatial width of the order of ~ 25λD, there is a small but finite electric potential drop, implying an average electric field generally directed away from the Sun. The IES wave forms, which have not been previously reported in the solar wind, are similar, although with a smaller amplitude, to the weak double layers observed in the auroral regions, and to the electrostatic solitary waves observed in other regions in the magnetosphere. We have also studied the solar wind conditions which favour the occurrence of the three kinds of waves: all these e.s. waves are observed more or less continuously in the whole solar wind (except in the densest regions where a parasite prevents the TDS observations). The type (wave packet or IES) of the observed LF waves is mainly determined by the proton temperature and by the direction of the magnetic field, which themselves depend on the latitude of WIND with respect to the heliospheric current sheet.Key words. Interplanetary physics (plasma waves and turbulence; solar wind plasma). Space plasma physics (electrostatic structures).

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