4,538 research outputs found
Heavy Leptons
A summary of our present knowledge about the new heavy lepton T is given
Orthogonal Polynomials from Hermitian Matrices
A unified theory of orthogonal polynomials of a discrete variable is
presented through the eigenvalue problem of hermitian matrices of finite or
infinite dimensions. It can be considered as a matrix version of exactly
solvable Schr\"odinger equations. The hermitian matrices (factorisable
Hamiltonians) are real symmetric tri-diagonal (Jacobi) matrices corresponding
to second order difference equations. By solving the eigenvalue problem in two
different ways, the duality relation of the eigenpolynomials and their dual
polynomials is explicitly established. Through the techniques of exact
Heisenberg operator solution and shape invariance, various quantities, the two
types of eigenvalues (the eigenvalues and the sinusoidal coordinates), the
coefficients of the three term recurrence, the normalisation measures and the
normalisation constants etc. are determined explicitly.Comment: 53 pages, no figures. Several sentences and a reference are added. To
be published in J. Math. Phy
Scattering by a contact potential in three and lower dimensions
We consider the scattering of nonrelativistic particles in three dimensions
by a contact potential which is defined
as the limit of . It is
surprising that it gives a nonvanishing cross section when and
. When the contact potential is approached by a spherical square
well potential instead of the above spherical shell one, one obtains basically
the same result except that the parameter that gives a nonvanishing
cross section is different. Similar problems in two and one dimensions are
studied and results of the same nature are obtained.Comment: REVTeX, 9 pages, no figur
Scattering states of a particle, with position-dependent mass, in a double heterojunction
In this work we obtain the exact analytical scattering solutions of a
particle (electron or hole) in a semiconductor double heterojunction -
potential well / barrier - where the effective mass of the particle varies with
position inside the heterojunctions. It is observed that the spatial dependence
of mass within the well / barrier introduces a nonlinear component in the plane
wave solutions of the continuum states. Additionally, the transmission
coefficient is found to increase with increasing energy, finally approaching
unity, whereas the reflection coefficient follows the reverse trend and goes to
zero.Comment: 7 pages, 6 figure
Anomaly Cancellation in 2+1 dimensions in the presence of a domainwall mass
A Fermion in 2+1 dimensions, with a mass function which depends on one
spatial coordinate and passes through a zero ( a domain wall mass), is
considered. In this model, originally proposed by Callan and Harvey, the gauge
variation of the effective gauge action mainly consists of two terms. One comes
from the induced Chern-Simons term and the other from the chiral fermions,
bound to the 1+1 dimensional wall, and they are expected to cancel each other.
Though there exist arguments in favour of this, based on the possible forms of
the effective action valid far from the wall and some facts about theories of
chiral fermions in 1+1 dimensions, a complete calculation is lacking. In this
paper we present an explicit calculation of this cancellation at one loop valid
even close to the wall. We show that, integrating out the ``massive'' modes of
the theory does produce the Chern-Simons term, as appreciated previously. In
addition we show that it generates a term that softens the high energy
behaviour of the 1+1 dimensional effective chiral theory thereby resolving an
ambiguity present in a general 1+1 dimensional theory.Comment: 17 pages, LaTex file, CU-TP-61
Effective-Mass Dirac Equation for Woods-Saxon Potential: Scattering, Bound States and Resonances
Approximate scattering and bound state solutions of the one-dimensional
effective-mass Dirac equation with the Woods-Saxon potential are obtained in
terms of the hypergeometric-type functions. Transmission and reflection
coefficients are calculated by using behavior of the wave functions at
infinity. The same analysis is done for the constant mass case. It is also
pointed out that our results are in agreement with those obtained in
literature. Meanwhile, an analytic expression is obtained for the transmission
resonance and observed that the expressions for bound states and resonances are
equal for the energy values .Comment: 20 pages, 6 figure
Variational Study of Weakly Coupled Triply Heavy Baryons
Baryons made of three heavy quarks become weakly coupled, when all the quarks
are sufficiently heavy such that the typical momentum transfer is much larger
than Lambda_QCD. We use variational method to estimate masses of the
lowest-lying bcc, ccc, bbb and bbc states by assuming they are Coulomb bound
states. Our predictions for these states are systematically lower than those
made long ago by Bjorken.Comment: 31 pages, 5 figure
Parity measurement of one- and two-electron double well systems
We outline a scheme to accomplish measurements of a solid state double well
system (DWS) with both one and two electrons in non-localised bases. We show
that, for a single particle, measuring the local charge distribution at the
midpoint of a DWS using an SET as a sensitive electrometer amounts to
performing a projective measurement in the parity (symmetric/antisymmetric)
eigenbasis. For two-electrons in a DWS, a similar configuration of SET results
in close-to-projective measurement in the singlet/triplet basis. We analyse the
sensitivity of the scheme to asymmetry in the SET position for some
experimentally relevant parameter, and show that it is realisable in
experiment.Comment: 18 Pages, to appear in PR
Low-lying spectra in anharmonic three-body oscillators with a strong short-range repulsion
Three-body Schroedinger equation is studied in one dimension. Its two-body
interactions are assumed composed of the long-range attraction (dominated by
the L-th-power potential) in superposition with a short-range repulsion
(dominated by the (-K)-th-power core) plus further subdominant power-law
components if necessary. This unsolvable and non-separable generalization of
Calogero model (which is a separable and solvable exception at L = K = 2) is
presented in polar Jacobi coordinates. We derive a set of trigonometric
identities for the potentials which generalizes the well known K=2 identity of
Calogero to all integers. This enables us to write down the related partial
differential Schroedinger equation in an amazingly compact form. As a
consequence, we are able to show that all these models become separable and
solvable in the limit of strong repulsion.Comment: 18 pages plus 6 pages of appendices with new auxiliary identitie
Representation reduction and solution space contraction in quasi-exactly solvable systems
In quasi-exactly solvable problems partial analytic solution (energy spectrum
and associated wavefunctions) are obtained if some potential parameters are
assigned specific values. We introduce a new class in which exact solutions are
obtained at a given energy for a special set of values of the potential
parameters. To obtain a larger solution space one varies the energy over a
discrete set (the spectrum). A unified treatment that includes the standard as
well as the new class of quasi-exactly solvable problems is presented and few
examples (some of which are new) are given. The solution space is spanned by
discrete square integrable basis functions in which the matrix representation
of the Hamiltonian is tridiagonal. Imposing quasi-exact solvability constraints
result in a complete reduction of the representation into the direct sum of a
finite and infinite component. The finite is real and exactly solvable, whereas
the infinite is complex and associated with zero norm states. Consequently, the
whole physical space contracts to a finite dimensional subspace with
normalizable states.Comment: 25 pages, 4 figures (2 in color
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