1,773 research outputs found
New Solvable Singular Potentials
We obtain three new solvable, real, shape invariant potentials starting from
the harmonic oscillator, P\"oschl-Teller I and P\"oschl-Teller II potentials on
the half-axis and extending their domain to the full line, while taking special
care to regularize the inverse square singularity at the origin. The
regularization procedure gives rise to a delta-function behavior at the origin.
Our new systems possess underlying non-linear potential algebras, which can
also be used to determine their spectra analytically.Comment: 19 pages, 4 figure
Coordinate Realizations of Deformed Lie Algebras with Three Generators
Differential realizations in coordinate space for deformed Lie algebras with
three generators are obtained using bosonic creation and annihilation operators
satisfying Heisenberg commutation relations. The unified treatment presented
here contains as special cases all previously given coordinate realizations of
and their deformations. Applications to physical problems
involving eigenvalue determination in nonrelativistic quantum mechanics are
discussed.Comment: 11 pages, 0 figure
Is the Lowest Order Supersymmetric WKB Approximation Exact for All Shape Invariant Potentials ?
It has previously been proved that the lowest order supersymmetric WKB
approximation reproduces the exact bound state spectrum of shape invariant
potentials. We show that this is not true for a new, recently discovered class
of shape invariant potentials and analyse the reasons underlying this breakdown
of the usual proof.Comment: 8 page
Chemistry of Lanthanons : Part XLIV- Isolation & Characterization of Coumarin-3- carboxylate Chelates of Lanthanons
361-36
Algebraic Shape Invariant Models
Motivated by the shape invariance condition in supersymmetric quantum
mechanics, we develop an algebraic framework for shape invariant Hamiltonians
with a general change of parameters. This approach involves nonlinear
generalizations of Lie algebras. Our work extends previous results showing the
equivalence of shape invariant potentials involving translational change of
parameters with standard potential algebra for Natanzon type
potentials.Comment: 8 pages, 2 figure
New Shape Invariant Potentials in Supersymmetric Quantum Mechanics
Quantum mechanical potentials satisfying the property of shape invariance are
well known to be algebraically solvable. Using a scaling ansatz for the change
of parameters, we obtain a large class of new shape invariant potentials which
are reflectionless and possess an infinite number of bound states. They can be
viewed as q-deformations of the single soliton solution corresponding to the
Rosen-Morse potential. Explicit expressions for energy eigenvalues,
eigenfunctions and transmission coefficients are given. Included in our
potentials as a special case is the self-similar potential recently discussed
by Shabat and Spiridonov.Comment: 8pages, Te
New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity
We discuss in some detail the self-similar potentials of Shabat and
Spiridonov which are reflectionless and have an infinite number of bound
states. We demonstrate that these self-similar potentials are in fact shape
invariant potentials within the formalism of supersymmetric quantum mechanics.
In particular, using a scaling ansatz for the change of parameters, we obtain a
large class of new, reflectionless, shape invariant potentials of which the
Shabat-Spiridonov ones are a special case. These new potentials can be viewed
as q-deformations of the single soliton solution corresponding to the
Rosen-Morse potential. Explicit expressions for the energy eigenvalues,
eigenfunctions and transmission coefficients for these potentials are obtained.
We show that these potentials can also be obtained numerically. Included as an
intriguing case is a shape invariant double well potential whose supersymmetric
partner potential is only a single well. Our class of exactly solvable
Hamiltonians is further enlarged by examining two new directions: (i) changes
of parameters which are different from the previously studied cases of
translation and scaling; (ii) extending the usual concept of shape invariance
in one step to a multi-step situation. These extensions can be viewed as
q-deformations of the harmonic oscillator or multi-soliton solutions
corresponding to the Rosen-Morse potential.Comment: 26 pages, plain tex, request figures by e-mai
Multimodal assessment of locus coeruleus integrity is associated with late-life memory performance
Time-Dependent and Steady-State Gutzwiller approach for nonequilibrium transport in nanostructures
We extend the time-dependent Gutzwiller variational approach, recently
introduced by Schir\`o and Fabrizio, Phys. Rev. Lett. 105 076401 (2010), to
impurity problems. Furthermore, we derive a consistent theory for the steady
state, and show its equivalence with the previously introduced nonequilibrium
steady-state extension of the Gutzwiller approach. The method is shown to be
able to capture dissipation in the leads, so that a steady state is reached
after a sufficiently long relaxation time. The time-dependent method is applied
to the single orbital Anderson impurity model at half-filling, modeling a
quantum dot coupled to two leads. In these first exploratory calculations the
Gutzwiller projector is limited to act only on the impurity. The strengths and
the limitations of this approximation are assessed via comparison with state of
the art continuous time quantum Monte Carlo results. Finally, we discuss how
the method can be systematically improved by extending the region of action of
the Gutzwiller projector.Comment: 13 pages, 6 figure
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