68 research outputs found
Potentials with Two Shifted Sets of Equally Spaced Eigenvalues and Their Calogero Spectrum
Motivated by the concept of shape invariance in supersymmetric quantum
mechanics, we obtain potentials whose spectrum consists of two shifted sets of
equally spaced energy levels. These potentials are similar to the
Calogero-Sutherland model except the singular term always falls
in the transition region and there is a delta-function
singularity at x=0.Comment: Latex, 12 pages, Figures available from Authors, To appear in Physics
Letters A. Please send requests for figures to [email protected] or
[email protected]
Galileo\u27s Contribution to Mechanics
Asim Gangopadhyaya writes about Galileo\u27s contributions to mechanics and physics in this chapter in Where Have All the Heavens Gone? Galileo\u27s Letter to the Grand Duchess Christina edited by John P. McCarthy and Edmondo F. Lupieri
The motion of two identical masses connected by an ideal string symmetrically placed over a corner
We introduce a novel, two-mass system that slides up an inclined plane while
its center of mass moves down. The system consists of two identical masses
connected by an ideal string symmetrically placed over a corner-shaped support.
This system is similar to a double-cone that rolls up an inclined set of
V-shaped rails. We find the double-cone's motion easy to demonstrate but
difficult to analyze. Our example here is more straightforward to follow, and
the experimental observations are in good agreement with the theoretical
predictions.Comment: 10 pages, 7 figures; Accepted for publication in American Journal of
Physic
Unintended consequences of imprecise Notation -- an example from mechanics
We present a conundrum that results from the imprecise use of notation for
partial derivatives. Taking an example from mechanics, we show that lack of
proper care in representing partial derivatives in Lagrangian and Hamiltonian
formulations paradoxically leads to two different values for the time
derivative of the canonical momentum. This problem also exists in other areas
of physics, such as thermodynamics
Barn and Pole paradox: revisited
We present two different paradoxes related to the length contraction in
special relativity and explain their resolution.Comment: 7 pages, 6 figures. To appear in Physics Education, IOP Scienc
Non-Central Potentials and Spherical Harmonics Using Supersymmetry and Shape Invariance
It is shown that the operator methods of supersymmetric quantum mechanics and
the concept of shape invariance can profitably be used to derive properties of
spherical harmonics in a simple way. The same operator techniques can also be
applied to several problems with non-central vector and scalar potentials. As
examples, we analyze the bound state spectra of an electron in a Coulomb plus
an Aharonov-Bohm field and/or in the magnetic field of a Dirac monopole.Comment: Latex, 12 pages. To appear in American Journal of Physic
Methods for Generating Quasi-Exactly Solvable Potentials
We describe three different methods for generating quasi-exactly solvable
potentials, for which a finite number of eigenstates are analytically known.
The three methods are respectively based on (i) a polynomial ansatz for wave
functions; (ii) point canonical transformations; (iii) supersymmetric quantum
mechanics. The methods are rather general and give considerably richer results
than those available in the current literature.Comment: 12 pages, LaTe
Superspace Ward Identities in Supersymmetric Gauge Theories
In superspace formulation of supersymmetric gauge theories, gauge invariance requires an infinite set of identities between the infinite set of renormalization constants. Using Ward identities in superspace, the same is derived. These identities at one loop level are also demonstrated
- âŠ