Showing papers on "Quantum state published in 1970"

Quantum stochastic processes ii

Abstract: We investigate properties of a class of quantum stochastic processes subject to a condition of irreducibility. These processes must be recurrent or transient and an equilibrium state can only exist in the former case. Every finite dimensional process is recurrent and it is possible to establish convergence in time to a unique equilibrium state. We study particularly the class of transition processes, which describe photon emissions of simple quantum mechanical systems in excited states.

The empirical determination of quantum states

Abstract: A common approach to quantum physics is enshrouded in a jargon which treats state vectors as attributes of physical systems and the concept of state preparation as a filtration scheme wherein a process involving measurement selects from a primordial assembly of systems those bearing some prescribed vector of interest. By contrast, the empirical experiences with which quantum theory is actually concerned relate measurement and preparation in quite an opposite manner. Reproducible preparation schemes are logically and temporally anterior to measurement acts. Measurement extracts numbers from systems prepared in a specified manner; these data are then regularized by the theory by means of a state concept which is in turn used to characterize succinctly the given mode of preparation. The present paper offers, in a simple spin model, a method for determining the quantum state that represents any reproducible preparation.

Theory of Particles with Variable Mass. II. Some Physical Consequences

Abstract: The formalism of the previous paper, in which mass and proper time are treated as independent dynamical variables in a canonical formalism, is shown to imply certain physical consequences. There will exist a mass vs proper time uncertainty relation; trajectories and proper time will be exactly determinable in an external gravitational field, while mass will be determinable in an external electromagnetic field; and conventional quantum mechanics will imply that equivalence is invalid for low‐lying quantum states. This leads to a second possible way to quantize a system in a gravitational field, which introduces a fundamental length. It is shown that it is possible to test for quantum interference effects of gravitational systems with present technology and conventional techniques, using the earth's gravitational field.

Quantum state memory

Abstract: A quantum state memory is described made up of a matrix suitable for conducting electromagnetic radiation along the paths of the matrix to the intersecting points. A suitable material is located at the intersecting points characterized by two quantum states which may be generated by atoms, molecules, or ions in liquids, solids, or gases. The switching between the quantum states is accomplished by subjecting the material at the intersecting points to electromagnetic radiation at two frequencies, in one case, and at a single frequency in the opposite case. Detection means are provided to determine the quantum state.

On the mathematical description of quantized fields

Abstract: We start from Haag's proposal to describe quantum fields at a point, corresponding to the heuristic description by means of their matrix elements (A(x)Φ‖Ψ) between vectors of a dense linear manifoldD of the Hilbert space. We particularize this idea, so that the sesquilinear functional that describes the field at a point may be considered as an element of the sequential completion of a space of operators, endowed with a suitable “D-weak” topology.

Renormalized Perturbation Theory for the Weakly Nonlinear Oscillator

Abstract: The problem of finding solutions for the weakly nonlinear quantum oscillator is investigated in the Heisenberg representation in one dimension. The perturbation method developed makes allowance for the nonisochronous nature of nonlinear oscillations and avoids at any level of approximation the secularity—terms increasing without bound as t → ∞—intrinsic to the usual type of iteration scheme. The treatment of the general quantum equation (d2/dt2 + ω2)x(t) = ef(x), for the Heisenberg position operator x(t), is first motivated by the classical analog. The iteration equations for the quantum case are derived, and the case f(x) = x3 is studied fully to order e, and partially to order e2.

Remark on phase-space distributions in quantum theory.

Abstract: If the choice is limited to quadratic forms, it is impossible to find representations of quantum states by positive distributions on phase space, either in the ordinary or in an extended “coarse‐grained” sense.

Position Expectation Values for an Electron in an Infinite Tilted Well

Abstract: A numerical technique is used to determine the manner in which the expectation values of position for an electron in an infinite tilted well depend on the potential gradient and quantum state of the system. The results are compared to the classical case and to the exact analytic expression for the special case in which the total energy of the electron is equal to the maximum value of the linear potential.