2,280 research outputs found
About maximally localized states in quantum mechanics
We analyze the emergence of a minimal length for a large class of generalized
commutation relations, preserving commutation of the position operators and
translation invariance as well as rotation invariance (in dimension higher than
one). We show that the construction of the maximally localized states based on
squeezed states generally fails. Rather, one must resort to a constrained
variational principle.Comment: accepted for publication in PR
Legal ramifications of intellectual property
Recent government policy changes that have resulted in encouraging or requiring increased intellectual property rights of Federally funded research and development activities are examined. The reasons for these changes are discussed, including considerations related to technology transfer, patent rights, copyrights, trade secrets, and computer software issues. The effect of these changes on traditional approaches to the dissemination of Federally funded scientific and technical information is considered and predictions concerning future trends in intellectual property rights are given
Comment on "Quantum mechanics of smeared particles"
In a recent article, Sastry has proposed a quantum mechanics of smeared
particles. We show that the effects induced by the modification of the
Heisenberg algebra, proposed to take into account the delocalization of a
particle defined via its Compton wavelength, are important enough to be
excluded experimentally.Comment: 2 page
Nonpointlike Particles in Harmonic Oscillators
Quantum mechanics ordinarily describes particles as being pointlike, in the
sense that the uncertainty can, in principle, be made arbitrarily
small. It has been shown that suitable correction terms to the canonical
commutation relations induce a finite lower bound to spatial localisation.
Here, we perturbatively calculate the corrections to the energy levels of an in
this sense nonpointlike particle in isotropic harmonic oscillators. Apart from
a special case the degeneracy of the energy levels is removed.Comment: LaTeX, 9 pages, 1 figure included via epsf optio
On the modification of Hamiltonians' spectrum in gravitational quantum mechanics
Different candidates of Quantum Gravity such as String Theory, Doubly Special
Relativity, Loop Quantum Gravity and black hole physics all predict the
existence of a minimum observable length or a maximum observable momentum which
modifies the Heisenberg uncertainty principle. This modified version is usually
called the Generalized (Gravitational) Uncertainty Principle (GUP) and changes
all Hamiltonians in quantum mechanics. In this Letter, we use a recently
proposed GUP which is consistent with String Theory, Doubly Special Relativity
and black hole physics and predicts both a minimum measurable length and a
maximum measurable momentum. This form of GUP results in two additional terms
in any quantum mechanical Hamiltonian, proportional to and
, respectively, where is the GUP
parameter. By considering both terms as perturbations, we study two quantum
mechanical systems in the framework of the proposed GUP: a particle in a box
and a simple harmonic oscillator. We demonstrate that, for the general
polynomial potentials, the corrections to the highly excited eigenenergies are
proportional to their square values. We show that this result is exact for the
case of a particle in a box.Comment: 11 pages, to appear in Europhysics Letter
Reduction to Practice of Space Inventions
The legal concept of actual reduction to practice can be a significant factor in obtaining patent protection for an invention. It is well established that to prove actual reduction to practice, it must be shown the invention worked as intended in its practical contemplated use; and the acts relied on for reduction to practice cannot occur in a foreign country.
To show that an invention worked as intended in its practical contemplated use, a complete operative embodiment must be constructed and subjected to some degree of testing; and depending on the circumstances this testing may be under conditions of actual use; in a simulated environment which duplicates the essential conditions of actual use, or in some instances it may be bench testing which does not simulate all the conditions of actual use. The type and degree of testing necessary to show reduction to practice is discussed, with emphasis on inventions intended to be used in a space environment.
Consideration is also given to situations where an invention may have been first actually reduced to practice in outer space, and whether this can be used to establish a date of invention under United States patent law. The extent of territorial sovereignty in the airspace above a nation\u27s boundaries is considered, along with the ramification of operation of the invention beyond this territorial sovereignty. It is concluded that reduction to practice in outer space is tantamount to reduction to practice in the United States, based on one of two theories: the operation of an integrated instrumentality, wherein the invention is not removed from the United States by reason of the spacecraft being necessarily distant; and a free space doctrine, wherein occurrences onboard the spacecraft remain under the jurisdiction and control of the launching or registrynation
Minimal Length Uncertainty Relation and Hydrogen Atom
We propose a new approach to calculate perturbatively the effects of a
particular deformed Heisenberg algebra on energy spectrum. We use this method
to calculate the harmonic oscillator spectrum and find that corrections are in
agreement with a previous calculation. Then, we apply this approach to obtain
the hydrogen atom spectrum and we find that splittings of degenerate energy
levels appear. Comparison with experimental data yields an interesting upper
bound for the deformation parameter of the Heisenberg algebra.Comment: 7 pages, REVTe
Algebraic {}-Integration and Fourier Theory on Quantum and Braided Spaces
We introduce an algebraic theory of integration on quantum planes and other
braided spaces. In the one dimensional case we obtain a novel picture of the
Jackson -integral as indefinite integration on the braided group of
functions in one variable . Here is treated with braid statistics
rather than the usual bosonic or Grassmann ones. We show that the definite
integral can also be evaluated algebraically as multiples of the
integral of a -Gaussian, with remaining as a bosonic scaling variable
associated with the -deformation. Further composing our algebraic
integration with a representation then leads to ordinary numbers for the
integral. We also use our integration to develop a full theory of -Fourier
transformation . We use the braided addition and braided-antipode to define a convolution product, and prove a
convolution theorem. We prove also that . We prove the analogous results
on any braided group, including integration and Fourier transformation on
quantum planes associated to general R-matrices, including -Euclidean and
-Minkowski spaces.Comment: 50 pages. Minor changes, added 3 reference
Hydrogen atom as an eigenvalue problem in 3D spaces of constant curvature and minimal length
An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the
Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is
considered from the perspective of the radial Schr\"odinger equations on 3D
spaces of any (either positive, zero or negative) constant curvature. Further
to Stevenson, we show in detail how to get the hypergeometric wavefunction for
the hydrogen atom case. Finally, we make a comparison between the ``space
curvature" effects and minimal length effects for the hydrogen spectrumComment: 6 pages, v
Vacuum entanglement enhancement by a weak gravitational field
Separate regions in space are generally entangled, even in the vacuum state.
It is known that this entanglement can be swapped to separated Unruh-DeWitt
detectors, i.e., that the vacuum can serve as a source of entanglement. Here,
we demonstrate that, in the presence of curvature, the amount of entanglement
that Unruh-DeWitt detectors can extract from the vacuum can be increased.Comment: 6 pages, 1 figur
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