124 research outputs found
Asymptotic behaviour of the probability density in one dimension
We demonstrate that the probability density of a quantum state moving freely
in one dimension may decay faster than 1/t. Inverse quadratic and cubic
dependences are illustrated with analytically solvable examples. Decays faster
than 1/t allow the existence of dwell times and delay times.Comment: 5 pages, one eps figure include
Duality and the Equivalence Principle of Quantum Mechanics
Following a suggestion by Vafa, we present a quantum-mechanical model for
S-duality symmetries observed in the quantum theories of fields, strings and
branes. Our formalism may be understood as the topological limit of Berezin's
metric quantisation of the upper half-plane H, in that the metric dependence
has been removed. Being metric-free, our prescription makes no use of global
quantum numbers. Quantum numbers arise only locally, after the choice of a
local vacuum to expand around. Our approach may be regarded as a manifestly non
perturbative formulation of quantum mechanics, in that we take no classical
phase space and no Poisson brackets as a starting point. The reparametrisation
invariance of H under SL(2,R) induces a natural SL(2,R) action on the quantum
mechanical operators that implements S-duality. We also link our approach with
the equivalence principle of quantum mechanics recently formulated by Faraggi
and Matone.Comment: 14 pages, JHEP styl
Comment on "Measurement of time of arrival in quantum mechanics"
The analysis of the model quantum clocks proposed by Aharonov et al. [Phys.
Rev. A 57 (1998) 4130 - quant-ph/9709031] requires considering evanescent
components, previously ignored. We also clarify the meaning of the operational
time of arrival distribution which had been investigated.Comment: 3 inlined figures; comment on quant-ph/970903
Transition from discrete to continuous time of arrival distribution for a quantum particle
We show that the Kijowski distribution for time of arrivals in the entire
real line is the limiting distribution of the time of arrival distribution in a
confining box as its length increases to infinity. The dynamics of the confined
time of arrival eigenfunctions is also numerically investigated and
demonstrated that the eigenfunctions evolve to have point supports at the
arrival point at their respective eigenvalues in the limit of arbitrarilly
large confining lengths, giving insight into the ideal physical content of the
Kijowsky distribution.Comment: Accepted for publication in Phys. Rev.
Generalizations of Kijowski's time-of-arrival distribution for interaction potentials
Several proposals for a time-of-arrival distribution of ensembles of
independent quantum particles subject to an external interaction potential are
compared making use of the ``crossing state'' concept. It is shown that only
one of them has the properties expected for a classical distribution in the
classical limit. The comparison is illustrated numerically with a collision of
a Gaussian wave packet with an opaque square barrier.Comment: 5 inlined figures: some typo correction
- …