3,454 research outputs found
Relativistic shape invariant potentials
Dirac equation for a charged spinor in electromagnetic field is written for
special cases of spherically symmetric potentials. This facilitates the
introduction of relativistic extensions of shape invariant potential classes.
We obtain the relativistic spectra and spinor wavefunctions for all potentials
in one of these classes. The nonrelativistic limit reproduces the usual
Rosen-Morse I & II, Eckart, Poschl-Teller, and Scarf potentials.Comment: Corrigendum: The last statement above equation (1) is now corrected
and replaced by two new statement
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
Graded extension of SO(2,1) Lie algebra and the search for exact solutions of Dirac equation by point canonical transformations
SO(2,1) is the symmetry algebra for a class of three-parameter problems that
includes the oscillator, Coulomb and Morse potentials as well as other problems
at zero energy. All of the potentials in this class can be mapped into the
oscillator potential by point canonical transformations. We call this class the
"oscillator class". A nontrivial graded extension of SO(2,1) is defined and its
realization by two-dimensional matrices of differential operators acting in
spinor space is given. It turns out that this graded algebra is the
supersymmetry algebra for a class of relativistic potentials that includes the
Dirac-Oscillator, Dirac-Coulomb and Dirac-Morse potentials. This class is, in
fact, the relativistic extension of the oscillator class. A new point canonical
transformation, which is compatible with the relativistic problem, is
formulated. It maps all of these relativistic potentials into the
Dirac-Oscillator potential.Comment: Replaced with a more potrable PDF versio
Supersymmetric quantum mechanics based on higher excited states
We generalize the formalism and the techniques of the supersymmetric (susy)
quantum mechanics to the cases where the superpotential is generated/defined by
higher excited eigenstates. The generalization is technically almost
straightforward but physically quite nontrivial since it yields an infinity of
new classes of susy-partner potentials, whose spectra are exactly identical
except for the lowest m+1 states, if the superpotential is defined in terms of
the (m+1)-st eigenfunction, with m=0 reserved for the ground state. It is shown
that in case of the infinite 1-dim potential well nothing new emerges (the
partner potential is still of P\"oschl-Teller type I, for all m), whilst in
case of the 1-dim harmonic oscillator we get a new class of infinitely many
partner potentials: for each m the partner potential is expressed as the sum of
the quadratic harmonic potential plus rational function, defined as the
derivative of the ratio of two consecutive Hermite polynomials. These partner
potentials of course have m singularities exactly at the locations of the nodes
of the generating (m+1)-st wavefunction. The susy formalism applies everywhere
between the singularities. A systematic application of the formalism to other
potentials with known spectra would yield an infinitely rich class of
"solvable" potentials, in terms of their partner potentials. If the potentials
are shape invariant they can be solved at least partially and new types of
analytically obtainable spectra are expected.
PACS numbers: 03.65.-w, 03.65.Ge, 03.65.SqComment: 15 pages LaTeX file, no figures, submitted to J. Phys. A: accepted
for publication
- mixing and spin dependent CSV potential
We construct the charge symmetry violating (CSV) nucleon-nucleon potential
induced by the -\o mixing due to the neutron-proton mass difference
driven by the loop. Analytical expression for for the two-body CSV
potential is presented containing both the central and non- central
interaction. We show that the tensor interaction can significantly
enhance the charge symmetry violating interaction even if momentum
dependent off-shell - mixing amplitude is considered. It is
also shown that the inclusion of form factors removes the divergence arising
out of the contact interaction. Consequently, we see that the precise size of
the computed scattering length difference depends on how the short range
aspects of the CSV potential are treated.Comment: Accepted for publication in Phys. Rev.
PCA based health indicator for remaining useful life prediction of wind turbine gearbox
Fault prognosis of wind turbine gearbox has received considerable attention as it predicts the remaining useful life which further allows the scheduling of maintenance strategies. However, the studies related towards the RUL prediction of wind turbine gearbox are limited, because of the complexity of gearbox, acute changes in the operating conditions and non-linear nature of the acquired vibration signals. In this study, a health indicator is constructed in order to predict the remaining useful life of the wind turbine gearbox. Run to fail experiments are performed on a laboratory scaled wind turbine gearbox of overall gear ratio 1:100. Vibration signals are acquired and decomposed through continuous wavelet transform to obtain the wavelet coefficients. Various statistical features are computed from the wavelet coefficients which return form high-dimensional input feature set. Principal component analysis is performed to reduce the dimensionality and principal components (PCs) are computed from the input feature set. PC1 is considered as the health indicator and subjected to further smoothening by linear rectification technique. Exponential degradation model is fit to the considered health indicator and the model is able to predict the RUL of the gearbox with an error percentage of 2.73 %
Scattering of relativistic particles with Aharonov-Bohm-Coulomb interaction in two dimensions
The Aharonov-Bohm-Coulomb potentials in two dimensions may describe the
interaction between two particles carrying electric charge and magnetic flux,
say, Chern--Simons solitons, or so called anyons. The scattering problem for
such two-body systems is extended to the relativistic case, and the scattering
amplitude is obtained as a partial wave series. The electric charge and
magnetic flux is (, ) for one particle and (, ) for the
other. When , and takes on integer
or half integer values, the partial wave series is summed up approximately to
give a closed form. The results exhibit some nonperturbative features and
cannot be obtained from perturbative quantum electrodynamics at the tree level.Comment: revtex, 11 pages, no figur
Stopping power of hot QCD plasma
The partonic energy loss has been calculated taking both the hard and soft
contributions for all the processes, revealing the importance of the
individual channels. Cancellation of the intermediate separation scale has been
exhibited. Subtleties related to the identical final state partons have
properly been taken into account. The estimated collisional loss is compared
with its radiative counter part. We show that there exists a critical energy
() below which the collisional loss is more than its radiative
counterpart. In addition, we present closed form formulas for both the
collision probabilities and the stopping power ()Comment: revised version, section added, 9pages with 5 figure
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