180 research outputs found
Propagation of Vortex Electron Wave Functions in a Magnetic Field
The physics of coherent beams of photons carrying axial orbital angular
momentum (OAM) is well understood and such beams, sometimes known as vortex
beams, have found applications in optics and microscopy. Recently electron
beams carrying very large values of axial OAM have been generated. In the
absence of coupling to an external electromagnetic field the propagation of
such vortex electron beams is virtually identical mathematically to that of
vortex photon beams propagating in a medium with a homogeneous index of
refraction. But when coupled to an external electromagnetic field the
propagation of vortex electron beams is distinctly different from photons. Here
we use the exact path integral solution to Schrodingers equation to examine the
time evolution of an electron wave function carrying axial OAM. Interestingly
we find that the nonzero OAM wave function can be obtained from the zero OAM
wave function, in the case considered here, simply by multipling it by an
appropriate time and position dependent prefactor. Hence adding OAM and
propagating can in this case be replaced by first propagating then adding OAM.
Also, the results shown provide an explicit illustration of the fact that the
gyromagnetic ratio for OAM is unity. We also propose a novel version of the
Bohm-Aharonov effect using vortex electron beams.Comment: 14 pages, 2 figures, submitted to Phys Rev
Ideal Linear Chain Polymers with Fixed Angular Momentum
The statistical mechanics of a linear non-interacting polymer chain with a
large number of monomers is considered with fixed angular momentum. The radius
of gyration for a linear polymer is derived exactly by functional integration.
This result is then compared to simulations done with a large number of
non-interacting rigid links at fixed angular momentum. The simulation agrees
with the theory up to finite size corrections. The simulations are also used to
investigate the anisotropic nature of a spinning polymer. We find universal
scaling of the polymer size along the direction of the angular momentum, as a
function of rescaled angular momentum.Comment: 7 pages, 3 figure
Theory of inelastic scattering of cold neutrons from liquid helium
A measurement of the energy losses of monoenergetic neutrons scattered from liquid He II would permit a determination of the energy-versus-momentum relation for the elementary excitations (phonons and rotons) in the liquid. A major part of the scattering at a fixed angle arises from production or annihilation of a single excitation and appears as sharp lines in the energy spectrum. From the position of these lines the energy-versus-momentum relation of the excitations can be inferred. Other processes, such as production or annihilation of multiple excitations, contribute a continuous background, and occur at a negligible rate if the incident neutrons are slow (λ~>4A) and the helium cold (T<2°K). The total cross-section data can be accounted for by production of single excitations; the theoretical cross section, computed from a wave function previously proposed to represent excitations, agrees with experiment over the entire energy range, within 30%. Line widths in the discrete spectrum are negligible at 1°K because of the long lifetime of phonons and rotons
Velocity acquired by an electron in a finite electric field in a polar crystal
The expectation value of the steady-state velocity acquired by an electron interacting with the longitudinal, optical phonons of a polar crystal in a finite electric field is analyzed quantum mechanically for arbitrary coupling strength, field strength, and temperature. The rate of loss of momentum by an electron drifting through the crystal in the applied field is expressed in a form in which the lattice coordinates (the phonons) have been eliminated exactly by path-integral methods. This expression is then evaluated by a path-integral approach similar to that used to calculate the impedance of electrons in polar crystals. We present numerical calculations of field (loss of energy per unit distance) versus velocity for three coupling strengths using the Fröhlich polaron model. In a single curve, all the expected phenomena appear, including a threshold field for producing hot electrons and a decreasing rate of energy loss with velocity for very fast electrons. Using only the experimentally measured values of the reststrahlen energy and the static and optical dielectric constants, we find an energy loss of 0.025 eV/Å for electrons near the threshold in Al2O3, which compares favorably with the experimental value of about 0.03 eV/Å. We conclude that optical-phonon scattering can indeed produce the high rate of energy loss that is present in tunnel-cathode structures
Feynman Lectures on the Strong Interactions
These twenty-two lectures, with exercises, comprise the extent of what was
meant to be a full-year graduate-level course on the strong interactions and
QCD, given at Caltech in 1987-88. The course was cut short by the illness that
led to Feynman's death. Several of the lectures were finalized in collaboration
with Feynman for an anticipated monograph based on the course. The others,
while retaining Feynman's idiosyncrasies, are revised similarly to those he was
able to check. His distinctive approach and manner of presentation are manifest
throughout. Near the end he suggests a novel, nonperturbative formulation of
quantum field theory in dimensions. Supplementary material is provided in
appendices and ancillary files, including verbatim transcriptions of three
lectures and the corresponding audiotaped recordings.Comment: 98 pages, 117 figures; Feynman's personal course notes and audio
files for lectures 15, 17, 18 available at
http://www.physics.mcgill.ca/~jcline/Feynman
Feynman Lectures on the Strong Interactions
These twenty-two lectures, with exercises, comprise the extent of what was meant to be a full-year graduate-level course on the strong interactions and QCD, given at Caltech in 1987-88. The course was cut short by the illness that led to Feynman's death. Several of the lectures were finalized in collaboration with Feynman for an anticipated monograph based on the course. The others, while retaining Feynman's idiosyncrasies, are revised similarly to those he was able to check. His distinctive approach and manner of presentation are manifest throughout. Near the end he suggests a novel, nonperturbative formulation of quantum field theory in D dimensions. Supplementary material is provided in appendices and ancillary files, including verbatim transcriptions of three lectures and the corresponding audiotaped recordings
An operator calculus having applications in quantum electrodynamics
An alteration in the notation used to indicate the order of operation of noncommuting quantities is suggested. Instead of the order being defined by the position on the paper, an ordering subscript is introduced so that AsBs′ means AB or BA depending on whether s exceeds s′ or vice versa. Then As can be handled as though it were an ordinary numerical function of s. An increase in ease of manipulating some operator expressions results. Connection to the theory of functionals is discussed in an appendix. Illustrative applications to quantum mechanics are made. In quantum electrodynamics it permits a simple formal understanding of the interrelation of the various present day theoretical formulations.
The operator expression of the Dirac equation is related to the author's previous description of positrons. An attempt is made to interpret the operator ordering parameter in this case as a fifth coordinate variable in an extended Dirac equation. Fock's parametrization, discussed in an appendix, seems to be easier to interpret.
In the last section a summary of the numerical constants appearing in formulas for transition probabilities is given
Very high-energy collisions of hadrons
Proposals are made predicting the character of longitudinal-momentum distributions in hadron collisions of extreme energies
Relativistic cut-off for quantum electrodynamics
A relativistic cut-off of high frequency quanta, similar to that suggested by Bopp, is shown to produce a finite invariant self-energy for a free electron. The electromagnetic line shift for a bound electron comes out as given by Bethe and Weissk opf's wave packet prescription. The scattering of an electron in a potential, without radiation, is discussed. The cross section remains finite. The problem of polarization of the vacuum is not solved. Otherwise, the results will in general agree essentially with those calculated by the prescription of Schwinger. An alternative cut-off procedure analogous to one proposed by Wataghin, which eliminates high frequency intermediate states, is shown to do the same things but to offer to solve vacuum polarization problems as well
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