28 research outputs found
Comment on "A 'local observables' method for wave mechanics applied to atomic hydrogen," by Peter Bowman [Am. J. Phys. 76, 1120-1129 (2008)]
This comment identifies a mistake in a paper by P. Bowman that claims that
the total angular momentum of the ground state of atomic hydrogen is 1.Comment: 2 pp. To be published in Am. J. Phy
The evolution of free wave packets
We discuss four general features of force-free evolution: (1) The spatial
spread of any packet changes with time in a very simple way. (2) Over
sufficiently short periods of time (whose duration is related to the spread in
momentum of the packet) the probability distribution moves but there is little
change in shape. (3) After a sufficiently long period (related to the initial
spatial spread) the packet settles into a simple form simply related to the
momentum distribution in the packet. In this asymptotic regime, the shape of
the probability distribution no longer changes except for its scale, which
increases linearly with the time. (4) There is an infinite denumerable set of
simple wave packets (the Hermite-Gauss packets) that do not change shape as
they evolve.Comment: 6 pages, 4 figures, didactic pape
Post-Newtonian Parameters from Alternative Theories of Gravity
Alternative theories of gravity have been recently studied in connection with
their cosmological applications, both in the Palatini and in the metric
formalism. The aim of this paper is to propose a theoretical framework (in the
Palatini formalism) to test these theories at the solar system level and
possibly at the galactic scales. We exactly solve field equations in vacuum and
find the corresponding corrections to the standard general relativistic
gravitational field. On the other hand, approximate solutions are found in
matter cases starting from a Lagrangian which depends on a phenomenological
parameter. Both in the vacuum case and in the matter case the deviations from
General Relativity are controlled by parameters that provide the Post-Newtonian
corrections which prove to be in good agreement with solar system experiments.Comment: 17 pages, no figure
The general relativistic Poynting-Robertson effect
The general relativistic version is developed for Robertson's discussion of
the Poynting-Robertson effect that he based on special relativity and Newtonian
gravity for point radiation sources like stars. The general relativistic model
uses a test radiation field of photons in outward radial motion with zero
angular momentum in the equatorial plane of the exterior Schwarzschild or Kerr
spacetime.Comment: 19 pages iop style, 8 eps figure files for 5 figure
Spacetime dynamics of spinning particles - exact electromagnetic analogies
We compare the rigorous equations describing the motion of spinning test
particles in gravitational and electromagnetic fields, and show that if the
Mathisson-Pirani spin condition holds then exact gravito-electromagnetic
analogies emerge. These analogies provide a familiar formalism to treat
gravitational problems, as well as a means for comparing the two interactions.
Fundamental differences are manifest in the symmetries and time projections of
the electromagnetic and gravitational tidal tensors. The physical consequences
of the symmetries of the tidal tensors are explored comparing the following
analogous setups: magnetic dipoles in the field of non-spinning/spinning
charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr-de Sitter
spacetimes. The implications of the time projections of the tidal tensors are
illustrated by the work done on the particle in various frames; in particular,
a reciprocity is found to exist: in a frame comoving with the particle, the
electromagnetic (but not the gravitational) field does work on it, causing a
variation of its proper mass; conversely, for "static observers," a stationary
gravitomagnetic (but not a magnetic) field does work on the particle, and the
associated potential energy is seen to embody the Hawking-Wald spin-spin
interaction energy. The issue of hidden momentum, and its counterintuitive
dynamical implications, is also analyzed. Finally, a number of issues regarding
the electromagnetic interaction and the physical meaning of Dixon's equations
are clarified.Comment: 32+11 pages, 5 figures. Edited and further improved version, with new
Section C.2 unveiling analogies for arbitrary spin conditions, and new Sec.
3.2.3 in the Supplement making connection to the post-Newtonian
approximation; former Sec. III.B.4 and Appendix C moved to the (reshuffled)
Supplement; references updated. The Supplement is provided in ancillary file.
Matches the final published versio