1,130 research outputs found
Effective polar potential in the central force Schrodinger equation
The angular part of the Schrodinger equation for a central potential is
brought to the one-dimensional 'Schrodinger form' where one has a kinetic
energy plus potential energy terms. The resulting polar potential is seen to be
a family of potentials characterized by the square of the magnetic quantum
number m. It is demonstrated that this potential can be viewed as a confining
potential that attempts to confine the particle to the xy-plane, with a
strength that increases with increasing m. Linking the solutions of the
equation to the conventional solutions of the angular equation, i.e. the
associated Legendre functions, we show that the variation in the spatial
distribution of the latter for different values of the orbital angular quantum
number l can be viewed as being a result of 'squeezing' with different
strengths by the introduced 'polar potential'.Comment: This is an author-created, un-copyedited version of an article
accepted for publication in European Journal of Physic
Scattering in Noncommutative Quantum Mechanics
We derive the correction due to noncommutativity of space on Born
approximation, then the correction for the case of Yukawa potential is
explicitly calculated. The correction depends on the angle of scattering. Using
partial wave method it is shown that the conservation of the number of
particles in elastic scattering is also valid in noncommutative spaces which
means that the unitarity relation is held in noncommutative spaces. We also
show that the noncommutativity of space has no effect on the optical theorem.
Finally we study Gaussian function potential in noncommutative spaces which
generates delta function potential as .Comment: 7 Pages, no figure, accepted for publication in Modern Physics
Letters
Intrinsic localized modes in the charge-transfer solid PtCl
We report a theoretical analysis of intrinsic localized modes in a
quasi-one-dimensional charge-transfer-solid (PtCl). We discuss strongly nonlinear features of resonant Raman
overtone scattering measurements on PtCl, arising from quantum intrinsic
localized (multiphonon) modes (ILMs) and ILM-plus-phonon states. We show, that
Raman scattering data displays clear signs of a non-thermalization of lattice
degrees-of-freedom, manifested in a nonequilibrium density of intrinsic
localized modes.Comment: 4 pages, 4 figures, REVTE
A perturbative treatment for the energy levels of neutral atoms
Energy levels of neutral atoms have been re-examined by applying an
alternative perturbative scheme in solving the Schrodinger equation for the
Yukawa potential model with a modified screening parameter. The predicted shell
binding energies are found to be quite accurate over the entire range of the
atomic number up to 84 and compare very well with those obtained within the
framework of hyper-virial-Pade scheme and the method of shifted large-N
expansion. It is observed that the new perturbative method may also be applied
to the other areas of atomic physics.Comment: 18 page
Squeezed States and Affleck Dine Baryogenesis
Quantum fluctuations in the post inflationary Affleck-Dine baryogenesis model
are studied. The squeezed states formalism is used to give evolution equations
for the particle and anti-particle modes in the early universe. The role of
expansion and parametric amplification of the quantum fluctuations on the
baryon asymmetry produced is investigated.Comment: 8 pages 9 figure
The Generalised Raychaudhuri Equations : Examples
Specific examples of the generalized Raychaudhuri Equations for the evolution
of deformations along families of dimensional surfaces embedded in a
background dimensional spacetime are discussed. These include string
worldsheets embedded in four dimensional spacetimes and two dimensional
timelike hypersurfaces in a three dimensional curved background. The issue of
focussing of families of surfaces is introduced and analysed in some detail.Comment: 8 pages (Revtex, Twocolumn format). Corrected(see section on string
worldsheets), reorganised and shortened slightl
On Dimensional Degression in AdS(d)
We analyze the pattern of fields in d+1 dimensional anti-de Sitter space in
terms of those in d dimensional anti-de Sitter space. The procedure, which is
neither dimensional reduction nor dimensional compactification, is called
dimensional degression. The analysis is performed group-theoretically for all
totally symmetric bosonic and fermionic representations of the anti-de Sitter
algebra. The field-theoretical analysis is done for a massive scalar field in
AdS(d+d) and massless spin one-half, spin one, and spin two fields in
AdS(d+1). The mass spectra of the resulting towers of fields in AdS(d) are
found. For the scalar field case, the obtained results extend to the shadow
sector those obtained by Metsaev in [1] by a different method.Comment: 30 page
Bouncing Neutrons and the Neutron Centrifuge
The recent observation of the quantum state of the neutron bouncing freely
under gravity allows some novel experiments. A method of purifying the ground
state is given, and possible applications to the measurement of the electric
dipole moment of the neutron and the short distance behaviour of gravity are
discussed.Comment: 7 pages, 7 figure
SWKB Quantization Rules for Bound States in Quantum Wells
In a recent paper by Gomes and Adhikari (J.Phys B30 5987(1997)) a matrix
formulation of the Bohr-Sommerfield quantization rule has been applied to the
study of bound states in one dimension quantum wells. Here we study these
potentials in the frame work of supersymmetric WKB (SWKB) quantization
approximation and find that SWKB quantization rule is superior to the modified
Bohr-Sommerfield or WKB rules as it exactly reproduces the eigenenergies.Comment: 8 page
Renormalization in Quantum Mechanics
We implement the concept of Wilson renormalization in the context of simple
quantum mechanical systems. The attractive inverse square potential leads to a
\b function with a nontrivial ultraviolet stable fixed point and the Hulthen
potential exhibits the crossover phenomenon. We also discuss the implementation
of the Wilson scheme in the broader context of one dimensional potential
problems. The possibility of an analogue of Zamolodchikov's function in
these systems is also discussed.Comment: 16 pages, UR-1310, ER-40685-760. (Additional references included.
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