9,458 research outputs found
Part of the D - dimensional Spiked harmonic oscillator spectra
The pseudoperturbative shifted - l expansion technique PSLET [5,20] is
generalized for states with arbitrary number of nodal zeros. Interdimensional
degeneracies, emerging from the isomorphism between angular momentum and
dimensionality of the central force Schrodinger equation, are used to construct
part of the D - dimensional spiked harmonic oscillator bound - states. PSLET
results are found to compare excellenly with those from direct numerical
integration and generalized variational methods [1,2].Comment: Latex file, 20 pages, to appear in J. Phys. A: Math. & Ge
Generalized inequalities on warped product submanifolds in nearly trans-Sasakian manifolds
In this paper, we study warped product submanifolds of nearly trans-Sasakian
manifolds. The non-existence of the warped product semi-slant submanifolds of
the type is shown, whereas some characterization and
new geometric obstructions are obtained for the warped products of the type
. We establish two general inequalities for the
squared norm of the second fundamental form. The first inequality generalizes
derived inequalities for some contact metric manifolds [16, 18, 19, 24], while
by a new technique, the second inequality is constructed to express the
relation between extrinsic invariant (second fundamental form) and intrinsic
invariant (scalar curvatures). The equality cases are also discussed.Comment: 16 page
Explosive Formation and Dynamics of Vapor Nanobubbles around a Continuously Heated Gold Nanosphere
We form sub-micrometer-sized vapor bubbles around a single laser heating gold
nanoparticle in a liquid and monitor them through optical scattering of a probe
laser. The fast, inertia-governed expansion is followed by a slower contraction
and disappearance after some tens of nanoseconds. In a narrow range of
illumination powers, bubble time traces show a clear echo signature. We
attribute it to sound waves released upon the initial explosion and reflected
by flat interfaces, hundreds of microns away from the particle. Echoes can
trigger new explosions. A steady state of nanobubble with a vapor shell
surrounding the heated nanoparticle can be reached by a proper time profile of
the heating intensity. Stable nanobubbles could have original applications for
light modulation and for enhanced optical-acoustic coupling in photoacoustic
microscopy
d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass
The d-dimensional generalization of the point canonical transformation for a
quantum particle endowed with a position-dependent mass in Schrodinger equation
is described. Illustrative examples including; the harmonic oscillator,
Coulomb, spiked harmonic, Kratzer, Morse oscillator, Poschl-Teller and Hulthen
potentials are used as reference potentials to obtain exact energy eigenvalues
and eigenfunctions for target potentials at different position-dependent mass
settings.Comment: 14 pages, no figures, to appear in J. Phys. A: Math. Ge
On computing joint invariants of vector fields
A constructive version of the Frobenius integrability theorem -- that can be
programmed effectively -- is given. This is used in computing invariants of
groups of low ranks and recover examples from a recent paper of Boyko, Patera
and Popoyvich \cite{BPP}
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