Temporal Ordering in Quantum Mechanics

We examine the measurability of the temporal ordering of two events, as well as event coincidences. In classical mechanics, a measurement of the order-of-arrival of two particles is shown to be equivalent to a measurement involving only one particle (in higher dimensions). In quantum mechanics, we find that diffraction effects introduce a minimum inaccuracy to which the temporal order-of-arrival can be determined unambiguously. The minimum inaccuracy of the measurement is given by dt=1/E where E is the total kinetic energy of the two particles. Similar restrictions apply to the case of coincidence measurements. We show that these limitations are much weaker than limitations on measuring the time-of-arrival of a particle to a fixed location.Comment: New section added, arguing that order-of-arrival can be measured more accurately than time-of-arrival. To appear in Journal of Physics

A Physical Realization of the Generalized PT-, C-, and CPT-Symmetries and the Position Operator for Klein-Gordon Fields

Generalized parity (P), time-reversal (T), and charge-conjugation (C)operators were initially definedin the study of the pseudo-Hermitian Hamiltonians. We construct a concrete realization of these operators for Klein-Gordon fields and show that in this realization PT and C operators respectively correspond to the ordinary time-reversal and charge-grading operations. Furthermore, we present a complete description of the quantum mechanics of Klein-Gordon fields that is based on the construction of a Hilbert space with a relativistically invariant, positive-definite, and conserved inner product. In particular we offer a natural construction of a position operator and the corresponding localized and coherent states. The restriction of this position operator to the positive-frequency fields coincides with the Newton-Wigner operator. Our approach does not rely on the conventional restriction to positive-frequency fields. Yet it provides a consistent quantum mechanical description of Klein-Gordon fields with a genuine probabilistic interpretation.Comment: 20 pages, published versio

Crystalline ground states for classical particles

Pair interactions whose Fourier transform is nonnegative and vanishes above a wave number K_0 are shown to give rise to periodic and aperiodic infinite volume ground state configurations (GSCs) in any dimension d. A typical three dimensional example is an interaction of asymptotic form cos(K_0 r)/r^4. The result is obtained for densities rho >= rho_d where rho_1=K_0/2pi, rho_2=(sqrt{3}/8)(K_0/pi)^2 and rho_3=(1/8sqrt{2})(K_0/pi)^3. At rho_d there is a unique periodic GSC which is the uniform chain, the triangular lattice and the bcc lattice for d=1,2,3, respectively. For rho>rho_d the GSC is nonunique and the degeneracy is continuous: Any periodic configuration of density rho with all reciprocal lattice vectors not smaller than K_0, and any union of such configurations, is a GSC. The fcc lattice is a GSC only for rho>=(1/6 sqrt{3})(K_0/pi)^3.Comment: final versio

Ionisation by quantised electromagnetic fields: The photoelectric effect

In this paper we explain the photoelectric effect in a variant of the standard model of non relativistic quantum electrodynamics, which is in some aspects more closely related to the physical picture, than the one studied in [BKZ]: Now we can apply our results to an electron with more than one bound state and to a larger class of electron-photon interactions. We will specify a situation, where ionisation probability in second order is a weighted sum of single photon terms. Furthermore we will see, that Einstein's equality $$E_{kin}=h\nu-\bigtriangleup E>0$$ for the maximal kinetic energy $E_{kin}$ of the electron, energy $h\nu$ of the photon and ionisation gap $\bigtriangleup E$ is the crucial condition for these single photon terms to be nonzero.Comment: 59 pages, LATEX2

Patients as researchers - innovative experiences in UK National Health Service research

Consumer involvement is an established priority in UK health and social care service development and research. To date, little has been published describing the process of consumer involvement and assessing ‘consumers’ contributions to research. This paper provides a practical account of the effective incorporation of consumers into a research team, and outlines the extent to which they can enhance the research cycle; from project development and conduct, through data analysis and interpretation, to dissemination. Salient points are illustrated using the example of their collaboration in a research project. Of particular note were consumers’ contributions to the development of an ethically enhanced, more robust project design, and enriched data interpretation, which may not have resulted had consumers not been an integral part of the research team

Dipoles in Graphene Have Infinitely Many Bound States

We show that in graphene charge distributions with non-vanishing dipole moment have infinitely many bound states. The corresponding eigenvalues accumulate at the edges of the gap faster than any power

Quantum Singularities in Horava-Lifshitz Cosmology

The recently proposed Horava-Lifshitz (HL) theory of gravity is analyzed from the quantum cosmology point of view. By employing usual quantum cosmology techniques, we study the quantum Friedmann-Lemaitre-Robertson-Walker (FLRW) universe filled with radiation in the context of HL gravity. We find that this universe is quantum mechanically nonsingular in two different ways: the expectation value of the scale factor $(t)$ never vanishes and, if we abandon the detailed balance condition suggested by Horava, the quantum dynamics of the universe is uniquely determined by the initial wave packet and no boundary condition at $a=0$ is indeed necessary.Comment: 13 pages, revtex, 1 figure. Final version to appear in PR

The Aharonov-Bohm Effect and Tonomura et al. Experiments. Rigorous Results

We study the Aharonov-Bohm effect under the conditions of the Tonomura et al. experiments, that gave a strong evidence of the physical existence of the Aharonov-Bohm effect, and we give the first rigorous proof that the classical Ansatz of Aharonov and Bohm is a good approximation to the exact solution of the Schroedinger equation. We provide a rigorous, quantitative, error bound for the difference in norm between the exact solution and the approximate solution given by the Aharonov-Bohm Ansatz. Our error bound is uniform in time. Using the experimental data, we rigorously prove that the results of the Tonomura et al. experiments, that were predicted by Aharonov and Bohm, actually follow from quantum mechanics. Furthermore, our results show that it would be quite interesting to perform experiments for intermediate size electron wave packets (smaller than the ones used in the Tonomura et al. experiments, that were much larger than the magnet) whose variance satisfies appropriate lower and upper bounds that we provide. One could as well take a larger magnet. In this case, the interaction of the electron wave packet with the magnet is negligible -the probability that the electron wave packet interacts with the magnet is smaller than $10^{-199}$- and, moreover, quantum mechanics predicts the results observed by Tonomura et al. with an error bound smaller than $10^{-99}$, in norm. Our error bound has a physical interpretation. For small variances it is due to Heisenberg's uncertainty principle and for large variances to the interaction with the magnet.Comment: 63 pages,5 figure

Energy bounds for the spinless Salpeter equation: harmonic oscillator

We study the eigenvalues E_{n\ell} of the Salpeter Hamiltonian H = \beta\sqrt(m^2 + p^2) + vr^2, v>0, \beta > 0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple semi-classical formula E = min_{r > 0} {v(P/r)^2 + \beta\sqrt(m^2 + r^2)} provides both upper and lower energy bounds for all the eigenvalues of the problem.Comment: 8 pages, 1 figur

Quantum Singularities Around a Global Monopole

The behavior of a massive scalar particle on the spacetime surrounding a monopole is studied from a quantum mechanical point of view. All the boundary conditions necessary to turn into self-adjoint the spatial portion of the wave operator are found and their importance to the quantum interpretation of singularities is emphasized.Comment: 5 pages, revte