3,723 research outputs found
Smooth double barriers in quantum mechanics
Quantum mechanical tunneling across smooth double barrier potentials modeled
using Gaussian functions, is analyzed numerically and by using the WKB
approximation. The transmission probability, resonances as a function of
incident particle energy, and their dependence on the barrier parameters are
obtained for various cases. We also discuss the tunneling time, for which we
obtain generalizations of the known results for rectangular barriers.Comment: 23 pages, 8 figures, a slightly reduced version to appear in American
Journal of Physics, references correcte
Almost-zero-energy Eigenvalues of Some Broken Supersymmetric Systems
For a quantum mechanical system with broken supersymmetry, we present a
simple method of determining the ground state when the corresponding energy
eigenvalue is sufficiently small. A concise formula is derived for the
approximate ground state energy in an associated, well-separated, asymmetric
double-well-type potential. Our discussion is also relevant for the analysis of
the fermion bound state in the kink-antikink scalar background.Comment: revised version, to be pubilshed in PR
- 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.
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
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