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 $\Delta x$ 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 $\alpha p^3$ and $\alpha^2 p^4$, respectively, where $\alpha \sim 1/M_{Pl}c$ 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

Algebraic {qq}-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 $q$-integral as indefinite integration on the braided group of functions in one variable $x$. Here $x$ is treated with braid statistics $q$ rather than the usual bosonic or Grassmann ones. We show that the definite integral $\int x$ can also be evaluated algebraically as multiples of the integral of a $q$-Gaussian, with $x$ remaining as a bosonic scaling variable associated with the $q$-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 $q$-Fourier transformation $F$. We use the braided addition $\Delta x=x\otimes 1+1\otimes x$ and braided-antipode $S$ to define a convolution product, and prove a convolution theorem. We prove also that $F^2=S$. We prove the analogous results on any braided group, including integration and Fourier transformation on quantum planes associated to general R-matrices, including $q$-Euclidean and $q$-Minkowski spaces.Comment: 50 pages. Minor changes, added 3 reference

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

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