Showing papers on "Quantum state published in 1980"

Positive quantum joint distributions

Abstract: We demonstrate the existence of positive phase space density functions which yield the quantum mechanical marginal distributions of position and momentum.

States and observables in relativistic quantum field theories

Abstract: We discuss two related issues pertaining to the foundations of relativistic quantum field theories. First: the question of observables; more particularly the question of what constraints, if any, are imposed upon the set of observables by the requirement of relativistic microcausality. It turns out that this requirement is in fact considerably less restrictive than has been supposed in the past. Second: the issue of physical states. We find that, in contrast to the nonrelativistic case, it is not possible to define the quantum state of a system in relativistic quantum field theories, because in this latter case no consistent description of how the state changes as the result of a measurement can be developed.

Reduced hamiltonian orbitals. III. Unitarily invariant decomposition of hermitian operators

Abstract: A decomposition of an N-particle operator as a sum of N + 1 components is defined such that, in the case of a model system employing a finite one-particle basis set, the decomposition is invariant under unitary transformations of the basis set. Applied to a two-particle Hamiltonian, this decomposition gives rise to the distinction between the independent-particle energy and the coupling energy defined in previous papers. Applied to the reduced density operator for a quantum state, the decomposition corresponds to partitioning the density into irreducible components. This partitioning is illustrated by graphs of electron density for the water molecule.

Stieltjes-Tchebycheff Moment-Theory Approach to Photoeffect Studies in Hilbert Space

Abstract: Hilbert space provides an appropriate mathematical framework for theoretical studies of quantum phenomena [1]. In spite of this, it is customary to employ so called improper vectors that satisfy asymptotic boundary conditions in solutions of scattering problems [2,3]. It has proved difficult to construct such scattering functions for Schroedinger problems in which noncentral and nonlocal forces are present, and in which the incident and target particles satisfy permutation symmetry. Since Ritz variational techniques employing L2 trial functions are particularly well-suited for bound-state calculations in such cases [4], there is considerable motivation to devise related Hilbert-space methods for studies of scattering in the presence of complicated forces.

Band model parameters for the parallel bands of linear triatomic molecules—I. Theory

Abstract: Generalized equations are developed for computing the band model parameters ( S d ), ( S 1 2 /D ) and ( 1 d ) for the parallel bands of linear triatomic molecules The convergence of these band-model parameters as a function of the number of quantum states included in a computation is discussed for the 43 μm CO2 band at various temperatures and wavenumbers Comparisons are made to previous theoretical calculations for the 43 μm CO2 band, where it is shown that an insufficient number of quantum states was included in the earlier work to insure convergence of the band-model parameters

The decay of coherent rotational states subject to random quantum measurements

Abstract: The influence of the measurement apparatus on the γ-decay of coherent rotational states is discussed. It is shown that the mathematical procedure, which has been devised to describe the decay of an unstable particle characterized by a unique quantum state, applies, with suitable changes, also to this case. For very short times, the decay probability still shows the pulses discussed in a previous paper where the influence of the environment was not taken into account. For long times, the interaction with the environment enforces a superposition of exponentials for the decay probability.

Detection of Quantum Signals by a Mismatched Receiver

Abstract: A quantum receiver is modelled as a harmonic oscillator imperfectly matched to the incident signal-bearing field. At the beginning of its interaction with the field the oscillator is primed by being placed in a predetermined quantum state. It is shown how to calculate the state of this oscillator at the end of the observation interval both in the presence and in the absence of an incident coherent signal. As examples the error probabilities of a binary on-off communication system with such a mismatched receiver are calculated (a) for a signal of known phase, the receiver primed with a two-photon coherent state, and (b) for a signal of random phase, the receiver primed with a number eigenstate. In both cases the error probability depends on the mean number of externally available signal photons when the number of photons in the priming state is very large, rather than on the smaller number that would actually be absorbed by the mismatched receiver unprimed.

Quantum mechanics based on position

Abstract: The only observational quantity which quantum mechanics needs to address islocation. The typical primitive observation on a microsystem (e.g., photon) isdetection at alocation (e.g., by a photomultiplier “looking at” a grating). To analyze an experiment, (a) form a conceptual ensemble of replicas of it, (b) assign a wave function (in “position representation”) to its initial condition, (c) evolve the wave function by the Schrodinger equation (known, once and for all, as a function of the system's composition), (d) compute the probability for particle detection at various times and places. The initial wave function is chosen on the basis of experience with such treatments. Key experiments are thus treated: (i) time-of-flight, (ii) Stern-Gerlach, (iii) Franck-Hertz, (iv) photon recoil, (v) photoionization. Quantum states, dynamical variables, and measurements, and the usual postulates about them, are superfluous. The explicit treatments are nonrelativistic; the existence of relativistic generalizations is left open.

“Model Hamiltonian for one- and two-dimensional superfluids”

Abstract: A model Hamiltonian describing bosons in one and two space dimensions interacting via a repulsive interparticle potential is shown to give rise to the phenomenon of superfluidity. The model has macroscopic occupation of infinitely many single-particle quantum states and the energy spectrum of the elementary excitations exhibits both phonon and roton features. Relations are found between the roton parameters, the speed of first sound and the condensate fraction where any two of them can be taken as independent variables. It is also shown that the type of condensate considered is not excluded by any rigorous proof.

Quantization as a Stability Problem

Abstract: Modern conceptions about structure of matter are dominated by quantum theory i.e. oy the idea that the energy of microsystems only changes by jumps (quantum transitions), where microsystems suddenly go from a stationary state to another, exchanging between them energy parcels.

On the photon position observable

Abstract: The localizability of the photon is considered in the framework of Ludwig’s axiomatic formulation of quantum mechanics, following the approach of Kraus. In particular it is discussed the construction of states localized in bounded regions of the space and the connection of the photon position observable with the configuration-space photon number operator used by Mandel in quantum optics.

Nested hilbert spaces, complex canonical transformations and resonances

Abstract: It has been shown that several techniques, applied to define a finite norm for Gamow states, can be deduced from a generalized description of quantum mechanics. The theory of nested Hilbert spaces realized through some specific complex canonical transformations is used in order to treat decaying states as generalized eigenstates of the Hamiltonian with complex eigenvalues.

Covariance and Quantum Physics-Need for a New Foundation of Quantum Theory?

Abstract: Starting from the fact that the traditional formulation of quantum mechanics in pictures (Heisenberg picture, Schrodinger picture, etc.) does not fulfil the requirements of covariance, the question of the deeper reasons of this problem is asked. Several arguments for a new foundation of quantum theory on the basis of the formulated “Principle of Fundamental Covariance”, combining the General Principle of Relativity (Principle of Coordinate-Covariance in space-time) and the Principle of State-Operator-Covariance (in the space of quantum states), are presented.

Classical solutions of non-linear σ-models and their quantum fluctuations

Abstract: I study the properties of O(N) and CPn−1 non-linear σ-MOELS in the two dimensional Euclidean space. All classical solutions of the equations of motion can be characterized and in the CPn−1 model they can be expressed in a simple and explicit way in terms of holomorphic vectors. The topological winding number and the action of the general CPn−1 solution can be evaluated and the latter turns out always to be an integer multiple of 2π. I further discuss the stability of the solutions and the problem of one-loop calculations of quantum fluctuations around classical solutions.

Comment on "On far-field quantum states in optical communication

Abstract: The nature of the conversion of a pure nonclassical transmitted quantum state into a mixed classical state at a remote receiver is discussed under assmnptions appropriate to a free-space optical communication system, with particular reference to a correspondence ^{1} containing misconceptions about a paper of the author's [1].