1,522 research outputs found
The Hazen Mammoth (Mammuthus columbi), Prairie County, Arkansas
In May 1965, mammoth remains were exposed during the excavation of a borrow pit for construction of Interstate Highway 40, 2 mi northeast of Hazen, Prairie County, Arkansas. The proboscidian remains consisted of a skull with tusks, mandibles, atlas and other skeletal elements. The vertebra material was scattered over approximately 150 m (1,600 sq ft) but was confined to a layer of red clayey-silt 6.7 m (22 ft) below the surface. No additional fauna or flora was recovered. The mammoth remains are referred to Mammuthus columbi (Falconer, 1857) on the basis of characteristics of the dentition, particularly the comparison of index of hypsodonty to functional plate density. Mammuthus columbi was widely distributed in southeast North America during the late part of the Pleistocene Epoch (Sangamon-Wisconsin Stages)
Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space
We solve explicitly the two-dimensional harmonic oscillator and the harmonic
oscillator in a background magnetic field in noncommutative phase-space without
making use of any type of representation. A key observation that we make is
that for a specific choice of the noncommutative parameters, the time reversal
symmetry of the systems get restored since the energy spectrum becomes
degenerate. This is in contrast to the noncommutative configuration space where
the time reversal symmetry of the harmonic oscillator is always broken.Comment: 7 pages Late
Generalized barker sequences
Correlation functions for binary digital systems - binary code and vector analysi
Hyperfine splitting in noncommutative spaces
We study the hyperfine splitting in the framework of the noncommutative
quantum mechanics (NCQM) developed in the literature. The results show
deviations from the usual quantum mechanics. We show that the energy difference
between two excited F = I + 1/2 and the ground F = I - 1/2 states in a
noncommutative space (NCS) is bigger than the one in the commutative case, so
the radiation wavelength in NCSs must be shorter than the radiation wavelength
in commutative spaces. We also find an upper bound for the noncommutativity
parameter.Comment: No figure
Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
In analogy with conventional quantum mechanics, non-commutative quantum
mechanics is formulated as a quantum system on the Hilbert space of
Hilbert-Schmidt operators acting on non-commutative configuration space. It is
argued that the standard quantum mechanical interpretation based on Positive
Operator Valued Measures, provides a sufficient framework for the consistent
interpretation of this quantum system. The implications of this formalism for
rotational and time reversal symmetry are discussed. The formalism is applied
to the free particle and harmonic oscillator in two dimensions and the physical
signatures of non commutativity are identified.Comment: 11 page
Spectrum of the non-commutative spherical well
We give precise meaning to piecewise constant potentials in non-commutative
quantum mechanics. In particular we discuss the infinite and finite
non-commutative spherical well in two dimensions. Using this, bound-states and
scattering can be discussed unambiguously. Here we focus on the infinite well
and solve for the eigenvalues and eigenfunctions. We find that time reversal
symmetry is broken by the non-commutativity. We show that in the commutative
and thermodynamic limits the eigenstates and eigenfunctions of the commutative
spherical well are recovered and time reversal symmetry is restored
Non-commutative Quantum Mechanics in Three Dimensions and Rotational Symmetry
We generalize the formulation of non-commutative quantum mechanics to three
dimensional non-commutative space. Particular attention is paid to the
identification of the quantum Hilbert space in which the physical states of the
system are to be represented, the construction of the representation of the
rotation group on this space, the deformation of the Leibnitz rule accompanying
this representation and the implied necessity of deforming the co-product to
restore the rotation symmetry automorphism. This also implies the breaking of
rotational invariance on the level of the Schroedinger action and equation as
well as the Hamiltonian, even for rotational invariant potentials. For
rotational invariant potentials the symmetry breaking results purely from the
deformation in the sense that the commutator of the Hamiltonian and angular
momentum is proportional to the deformation.Comment: 21 page
Variations on the Planar Landau Problem: Canonical Transformations, A Purely Linear Potential and the Half-Plane
The ordinary Landau problem of a charged particle in a plane subjected to a
perpendicular homogeneous and static magnetic field is reconsidered from
different points of view. The role of phase space canonical transformations and
their relation to a choice of gauge in the solution of the problem is
addressed. The Landau problem is then extended to different contexts, in
particular the singular situation of a purely linear potential term being added
as an interaction, for which a complete purely algebraic solution is presented.
This solution is then exploited to solve this same singular Landau problem in
the half-plane, with as motivation the potential relevance of such a geometry
for quantum Hall measurements in the presence of an electric field or a
gravitational quantum well
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