535 research outputs found
On the role of coherent states in quantum foundations
Coherent states, and the Hilbert space representations they generate, provide
ideal tools to discuss classical/quantum relationships. In this paper we
analyze three separate classical/quantum problems using coherent states, and
show that useful connections arise among them. The topics discussed are: (1) a
truly natural formulation of phase space path integrals; (2) how this analysis
implies that the usual classical formalism is ``simply a subset'' of the
quantum formalism, and thus demonstrates a universal coexistence of both the
classical and quantum formalisms; and (3) how these two insights lead to a
complete analytic solution of a formerly insoluble family of nonlinear quantum
field theory models.Comment: ICQOQI'2010, Kiev, Ukraine, May-June 2010, Conference Proceedings (9
pages
Coherent states for continuous spectrum operators with non-normalizable fiducial states
The problem of building coherent states from non-normalizable fiducial states
is considered. We propose a way of constructing such coherent states by
regularizing the divergence of the fiducial state norm. Then, we successfully
apply the formalism to particular cases involving systems with a continuous
spectrum: coherent states for the free particle and for the inverted oscillator
are explicitly provided. Similar ideas can be used for other
systems having non-normalizable fiducial states.Comment: 17 pages, typos corrected, references adde
Coherent State Approach to Time Reparameterization Invariant Systems
For many years coherent states have been a useful tool for understanding
fundamental questions in quantum mechanics. Recently, there has been work on
developing a consistent way of including constraints into the phase space path
integral that naturally arises in coherent state quantization. This new
approach has many advantages over other approaches, including the lack of any
Gribov problems, the independence of gauge fixing, and the ability to handle
second-class constraints without any ambiguous determinants. In this paper, I
use this new approach to study some examples of time reparameterization
invariant systems, which are of special interest in the field of quantum
gravity
Distorted Heisenberg Algebra and Coherent States for Isospectral Oscillator Hamiltonians
The dynamical algebra associated to a family of isospectral oscillator
Hamiltonians is studied through the analysis of its representation in the basis
of energy eigenstates. It is shown that this representation becomes similar to
that of the standard Heisenberg algebra, and it is dependent of a parameter
. We name it {\it distorted Heisenberg algebra}, where is the
distortion parameter. The corresponding coherent states for an arbitrary
are derived, and some particular examples are discussed in full detail. A
prescription to produce the squeezing, by adequately selecting the initial
state of the system, is given.Comment: 21 pages, Latex, 3 figures available as hard copies upon request from
the first Autho
Adiabatic Motion of a Quantum Particle in a Two-Dimensional Magnetic Field
The adiabatic motion of a charged, spinning, quantum particle in a two -
dimensional magnetic field is studied. A suitable set of operators generalizing
the cinematical momenta and the guiding center operators of a particle moving
in a homogeneous magnetic field is constructed. This allows us to separate the
two degrees of freedom of the system into a {\sl fast} and a {\sl slow} one, in
the classical limit, the rapid rotation of the particle around the guiding
center and the slow guiding center drift. In terms of these operators the
Hamiltonian of the system rewrites as a power series in the magnetic length
\lb=\sqrt{\hbar c\over eB} and the fast and slow dynamics separates. The
effective guiding center Hamiltonian is obtained to the second order in the
adiabatic parameter \lb and reproduces correctly the classical limit.Comment: 17 pages, LaTe
Coherent states for the hydrogen atom
We construct wave packets for the hydrogen atom labelled by the classical
action-angle variables with the following properties. i) The time evolution is
exactly given by classical evolution of the angle variables. (The angle
variable corresponding to the position on the orbit is now non-compact and we
do not get exactly the same state after one period. However the gross features
do not change. In particular the wave packet remains peaked around the labels.)
ii) Resolution of identity using this overcomplete set involves exactly the
classical phase space measure. iii) Semi-classical limit is related to
Bohr-Sommerfield quantization. iv) They are almost minimum uncertainty wave
packets in position and momentum.Comment: 9 pages, 2 figures, minor change in language and journal reference
adde
A conjugate for the Bargmann representation
In the Bargmann representation of quantum mechanics, physical states are
mapped into entire functions of a complex variable z*, whereas the creation and
annihilation operators and play the role of
multiplication and differentiation with respect to z*, respectively. In this
paper we propose an alternative representation of quantum states, conjugate to
the Bargmann representation, where the roles of and
are reversed, much like the roles of the position and momentum operators in
their respective representations. We derive expressions for the inner product
that maintain the usual notion of distance between states in the Hilbert space.
Applications to simple systems and to the calculation of semiclassical
propagators are presented.Comment: 15 page
Coherent State Approach to Quantum Clocks
The ``problem of time'' has been a pressing issue in quantum gravity for some
time. To help understand this problem, Rovelli proposed a model of a two
harmonic oscillators system where one of the oscillators can be thought of as a
``clock'' for the other oscillator thus giving a natural time reference frame
for the system. Recently, the author has constructed an explicit form for the
coherent states on the reduced phase space of this system in terms of Klauder's
projection operator approach. In this paper, by using coherent state
representations and other tools from coherent state quantization, I investigate
the construction of gauge invariant operators on this reduced phase space, and
the ability to use a quantum oscillator as a ``clock.''Comment: 13 pages, Late
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