Showing papers on "Quantum state published in 1977"
TL;DR: The form of the wavefunction psi for a semiclassical regular quantum state (associated with classical motion on an N-dimensional torus in the 2N-dimensional phase space) is very different from the form of psi for an irregular state associated with stochastic classical motion in all or part of the (2N-1) energy surface in phase space as discussed by the authors.
Abstract: The form of the wavefunction psi for a semiclassical regular quantum state (associated with classical motion on an N-dimensional torus in the 2N-dimensional phase space) is very different from the form of psi for an irregular state (associated with stochastic classical motion on all or part of the (2N-1)-dimensional energy surface in phase space). For regular states the local average probability density Pi rises to large values on caustics at the boundaries of the classically allowed region in coordinate space, and psi exhibits strong anisotropic interference oscillations. For irregular states Pi falls to zero (or in two dimensions stays constant) on 'anticaustics' at the boundary of the classically allowed region, and psi appears to be a Gaussian random function exhibiting more moderate interference oscillations which for ergodic classical motion are statistically isotropic with the autocorrelation of psi given by a Bessel function.
1,068 citations
TL;DR: In this article, it was shown that a continuous representation of quantum mechanics exists on a given fuzzy phase space if an only if the corresponding confidence functions for position and momentum measurements satisfy the Heisenberg uncertainty relations.
Abstract: The problem of expressing quantum mechanical expectation values as averages with respect to nonnegative density functions on phase space, by analogy with classical mechanics, is reexamined in the light of some earlier work on fuzzy phase spaces. It is shown that such phase space representations are possible if ordinary phase space is replaced by a so‐called fuzzy phase space, on which the usual marginal distribution functions are redefined to conform to the fact that arbitrarily precise simultaneous measurements on position and momentum are not compatible with quantum mechanics. In the process a generalization of Wigner’s theorem on the nonexistence of phase space representations of quantum mechanics, which also satisfy the standard (classical) marginality conditions in position and momentum, is obtained. It is shown that a (continuous) representation of quantum mechanics exists on a given fuzzy phase space if an only if the corresponding confidence functions for position and momentum measurements satisfy the Heisenberg uncertainty relations.
153 citations
TL;DR: In this article, the effect of selective laser radiation on matter has been studied. But this work is limited to a single quantum state of an atom or a molecule with excitation energy in the range 0.1 to 10 eV.
Abstract: Current progress with tunable lasers has made possible the selective excitation of practically any single quantum state of an atom or a molecule with excitation energy in the range 0.1 to 10 eV. Already we can obtain coherent radiation with sufficient intensity to excite a significant fraction of an atomic or molecular sample into chosen quantum states in the wavelength range 2000 A to 20 microns. Systematic studies of the effect of selective laser radiation on matter have been under way since around 1969 and 1970, when substantial progress in the art of quantum electronics made the experiments possible.
68 citations
Journal Article•
TL;DR: In this article, a general theorem is presented which says that from a sequence of Euclidean Green's functions satisfying a special form of the Osterwalder-Schrader axioms a local net of observable algebras satisfying all the Haag-Kastler axiomas can be reconstructed.
Abstract: A general theorem is presented which says that from a sequence of Euclidean Green’s functions satisfying a special form of the Osterwalder-Schrader axioms a local net of observable algebras satisfying all the Haag-Kastler axioms can be reconstructed. In the course of the proof a new sufficient condition for the bounded functions of two commuting, unbounded selfadjoint operators to commute is derived.
47 citations
TL;DR: In this article, it was shown that two-dimensional quantum kinks are statistical "schizons" and exist in the same Hilbert space either as bosons or as fermions.
34 citations
TL;DR: In this article, the transverse magnetoresistance of Mg was calculated from first principles for the special case in which H is parallel to a [10.............. �� ��\bar 1$$====== 0]-type axis and J is parallel with a [11.............. ¯¯\bar 2$$¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 0]- type axis, and it was shown that two distinct regimes of quantum transport exist for these oscillations.
Abstract: A new quantitative theory is developed to calculate from first principles the transverse magnetoresistance of Mg for the special case in whichH is parallel to a [10
$$\bar 1$$
0]-type axis andJ is parallel to a [11
$$\bar 2$$
0]-type axis. For this case, magnetic breakdown produces a multiply coupled network of interfering electron trajectories which generate large-amplitude quantum oscillations in the transverse magnetoresistance. It is shown that two distinct regimes of quantum transport exist for these oscillations and that this theory can be used to derive the electron quantum state lifetime τ from experimental data. The sensitivity of this effect to τ extends the experimentally accessible range by four orders of magnitude from about 10
−12
to 10
−8
sec. In addition, since the quantum interference oscillations are essentially insensitive to the temperature dependence of the Fermi-Dirac distribution function, this effect is ideally suited to study the quantum state lifetime dependence on electron-electron scattering.
27 citations
Journal Article•
26 citations
TL;DR: In this article, the Hilbert space formalism of quantum mechanics can be derived as a corrected form of probability theory, which yields the Schrodinger equation for a particle in an electromagnetic field and exhibits a relationship of this equation to Markov processes.
Abstract: It is shown that the Hilbert space formalism of quantum mechanics can be derived as a corrected form of probability theory. These constructions yield the Schrodinger equation for a particle in an electromagnetic field and exhibit a relationship of this equation to Markov processes. The operator formalism for expectation values is shown to be related to anL2 representation of marginal distributions and a relationship of the commutation rules for canonically conjugate observables to a topological relationship of two manifolds is indicated.
20 citations
TL;DR: The notion of relative compatibility was introduced in this article, where compatibility is construed as relative to individual quantum states, and the compatibility domain of two observables is defined to be the set of states relative to which A and B are compatible.
Abstract: The notion of relative compability is introduced, according to which compatibility is construed as relative to individual quantum states. The compatibility domain of two observablesA, B is defined to be the set com(A, B) of states relative to whichA andB are compatible. Three basic categories of relative compatibility are then defined according to the character of com(A, B): absolute compatibility (ordinary compatibility), absolute incompatibility, and partial compatibility. Then com(A, B) is seen to be a subspace of Hilbert space invariant underA andB; being a subspace, it corresponds to a quantum binary observable (projection), denotedc(A, B). IfA andB are themselves binary observables, thenc(A, B) is expressible as a quantum logical compound ofA andB using the lattice operations meet, join, and orthocomplement. This suggests extending the notion of relative compatibility to the theory of orthomodular lattices, as well as to more general lattice-theoretic formulations of quantum mechanics.
16 citations
TL;DR: In this article, a line shape comparison between the experimentally observed magnetoresistance oscillations and theoretical calculations based on the stacked-mirror model of quantum transport is presented, which provides direct evidence for the existence of long-range quantum phase coherence of the electron states in the Mg crystal.
Abstract: The quantum interferometer oscillations observed in the transverse magnetoresistance of Mg at liquid helium temperatures forJ∥[11\(\bar 1\)0] andH∥[1\(\bar 2\)00] have been experimentally investigated in detail. A new method of analyzing these quantum interference oscillations has been developed which permits direct line shape comparison between the experimentally observed magnetoresistance oscillations and theoretical calculations based on the stacked-mirror model of quantum transport. By using the stacked-mirror model in conjunction with the line shape comparison technique, virtually all of the approximations made in the initial studies of the quantum interferometer have been eliminated. Distinct and striking line shape changes in the magnetoresistance oscillations, critically dependent on the angle between the direction of the applied magnetic field and the basal plane of the Mg crystal, have also been observed and analyzed. This phenomenon provides direct evidence for the existence of long-range quantum phase coherence of the electron states in the Mg crystal over dimensions of ∼0.3 mm, corresponding to a quantum state lifetime τ of ∼3.5×10−10 sec. Experimental values for the three magnetic breakdown parameters that characterize the quantum interferometer in pure Mg areH1(kH=0)=3000±75 G,H2(kH=0)=10,000±1500 G, andH3(kH=0)=1000±250 G. Experimental evidence is also presented which shows a magnetic field dependence of the quantum state lifetime for some of the crystals studied.
TL;DR: In this paper, the authors compared the predictions of first principles theory and the experimental results in these two regimes, and showed that the theory not only predicts the qualitative behavior correctly but also provides a quantitatively accurate description for the transverse magnetoresistance.
Abstract: The “on-axis” and “off-axis” regimes of quantum transport discussed theoretically in the preceding paper in this journal have been observed experimentally. The observation of the “on-axis” regime required magnetic field alignment to within an accuracy of ±0.002° of the basal plane. The data for the “off-axis” regime indicate that the electron quantum state lifetime for this crystal is about 5×10−10 sec at 4.2 K. A comparison between the predictions of first principles theory and the experimental results in these two regimes shows that the theory not only predicts the qualitative behavior correctly but also provides a quantitatively accurate description for the transverse magnetoresistance.
TL;DR: In this paper, the reflection and transmission of a wave on a two-dimensional barrier is studied quantum mechanically and semiclassically, and the transition probabilities for transitions between the different quantum states can, in the model considered here, be evaluated analytically.
Abstract: The reflection and transmission of a wave on a two‐dimensional barrier is studied quantum mechanically and semiclassically. The simple model consists of two degrees of freedom. One of them contains a barrier (of the Eckart type); the second allows only a bound motion in discrete quantum states. These two degrees of freedom are coupled. The transition probabilities for transitions between the different quantum states can, in the model considered here, be evaluated analytically, both quantum mechanically and semiclassically. Several of the so called uniform semiclassical approximations and also the initial value integral representation for the semiclassical transition amplitudes are considered and compared to the exact quantum mechanical results. Some new insight on the semiclassical treatment of the tunneling process is gained, specially concerning the proper choice of the integration path for the initial value integral representation of the transition amplitudes.
TL;DR: In this article, a kink state which is an eigenstate of the Hamiltonian up to order √ λ was constructed in one space dimension with spontaneously broken symmetry.
TL;DR: In this paper, the authors considered the quantum expansion around a classical moving extended object using as a specific example the moving kink solution of the spontaneously broken φ4 theory in one space dimension.
TL;DR: In this article, a kinetic theory for quantum state diffusion in a simple polyatomic gas not at equilibrium is formulated, and the analogs of the Stefan-Maxwell equations are derived in two representations: in the first, a basis set for expanding the density matrix is chosen that is closest to the phenomenological description of quantum diffusion and yields easily recognizable generalizations of the binary diffusion coefficients.
Abstract: A kinetic theory is formulated for quantum state diffusion in a simple polyatomic gas not at equilibrium. The analogs of the Stefan–Maxwell equations are derived in two representations: in the first, a basis set for expanding the density matrix is chosen that is closest to the phenomenological description of quantum state diffusion and yields easily recognizable generalizations of the binary diffusion coefficients, now tensors, as well as source–sink terms, which is a new feature. In the second, a rotationally adapted basis set is used. Finally, the effect of exchange symmetry is discussed briefly.
TL;DR: In this paper, the concepts of measurement and measurable quantity are discussed and a probabilistic interpretation independent of the arrow of time is recommended and a definition of quantizable physical systems is given.
Abstract: The concepts of measurement and measurable quantity are discussed. A probabilistic interpretation independent of the arrow of time is recommended and a definition of quantizable physical systems is given. The space of states of information about the physical system is Schwarz space rather than Hilbert space.
TL;DR: In this paper, a fundamental assumption in the Dirac formulation of quantum mechanics, namely that the states of a physical system at a particular time are mathematically represented by unit vectors in Hilbert space, can be deduced from certain aspects of experimental procedures and of the observed outcome of quantum mechanical experiments.
Abstract: We show how a fundamental assumption in the Dirac formulation of quantum mechanics, namely that the states of a physical system at a particular time are mathematically represented by unit vectors in Hilbert space, can be deduced from certain aspects of our experimental procedures and of the observed outcome of quantum mechanical experiments. Our assumptions have clear empirical meaning and the results hold true for any dimensionality of the system, without anomalies in low dimensions which exist in the two well‐known axiomatic approaches to quantum mechanics. The propositional logic approach of Birkhoff and von Neumann does not work for quantum systems of dimension less than four and requires an assumption which does not have an empirical basis. Jordan algebra axioms, on the other hand, also lead to anomalies in low dimensions and, moreover, are formal and cannot be directly physically interpreted. In our work it was possible to avoid these shortcomings.
TL;DR: In this paper, it was shown that the decision to represent the fundamental events of quantum theory by vectors in a Hilbert space uniquely determines the form of any probability measure over the set of events.
Abstract: It is shown that merely the decision to represent the fundamental events of quantum theory by vectors in a Hilvert space uniquely determines the form of any probability measure over the set of events. The proof proceeds by showing that any nonnegative meausre on the vectors of a Hilbert space, for which the sum of the measures on the vectors of any complete orthonormal set is 1, takes the usual form damanded by quantum theory. This result represents a considerable strengthening of one of the consequences of Gleason’s theorem.
TL;DR: In this article, the authors show that for quantum systems of dimension less than four, there are no low-dimensional anomalies and the assumptions have clear empirical meaning, whereas the Jordan algebra approach, which provides the same limitations on the field, also suffers from anomalies in low dimensions.
Abstract: The well‐known limitations on the field of the quantum mechanical vector space, which, within the framework of the propositional logic of Birkhoff and von Neumann, can be obtained only for systems of dimension greater than or equal to four, are obtained here for all dimensions. The propositional logic fails to provide any information about the quantum systems of dimension less than four and, moreover, one does not know the empirical meaning of one of its basic assumptions. The Jordan algebra approach, on the other hand, which provides the same limitations on the field, also suffers from anomalies in low dimensions and is altogether formal rather than physical. In the present work, which is based on a recent study of the topological properties of quantum states, there are no low‐dimensional anomalies and the assumptions have clear empirical meaning.
TL;DR: In this paper, an operator which transforms quantum state functions from inertial to certain noninertial reference frames is presented, which is applied to solve two well-known problems: (1) the stationary state wave functions for a particle in a uniform gravitational field; (2) the motion and spreading of a Gaussian wave packet in uniform gravitational fields.
Abstract: An operator which transforms quantum state functions from inertial to certain noninertial reference frames is presented. This operator is applied to solve two well‐known problems: (1) the stationary state wave functions for a particle in a uniform gravitational field; (2) the motion and spreading of a Gaussian wave packet in a uniform gravitational field. The salient features of both analyses are discussed.
TL;DR: In this paper, a positive-operator-valued measure is constructed that has the same statistical properties as an observable defined on a Hilbert space that has a straightforward probabilistic interpretation.
Abstract: This paper is concerned with positive-operator-valued measures that are generated by modeling quantum measurements in which it is not possible to avoid residual experimental errors. A positive-operator-valued measure is constructed that has the same statistical properties as an observable defined on a Hilbert space that has a straightforward probabilistic interpretation.
TL;DR: The improved version of the Einstein-Schrodinger equation of quantum gravity found by one of us is solved in the linear approximation in this paper, but the solution differs from that obtained by Kuchař for the original version by an additional quantum effect: the energy, as deduced from measurements of the gravitational potential at infinity, has an error function probability distribution about its eigenvalue.
Abstract: The improved version of the Einstein-Schrodinger equation of quantum gravity found by one of us is solved in the linear approximation The solution differs from that obtained by K Kuchař for the original version of the equation by an additional quantum effect: The energy, as deduced from measurements of the gravitational potential at infinity, has an error function probability distribution about its eigenvalue The higher approximations are also considered and the appearance of a third quantum number, possibly related to the transition matrix, is deduced
TL;DR: In this paper, the authors draw attention to a series of papers that have appeared during the last years, in which the author criticized the usual scheme of quantum theory (Heisenberg picture, Schrodinger picture, etc.) and presented a new foundation of the basic laws of quantum physics, obeying the principle of fundamental covariance.
Abstract: If one accepts Einstein's general principle of relativity (covariance principle) also for the sphere of microphysics (quantum mechanics, quantum field theory, theory of elementary particles), one has to ask how far the fundamental laws of traditional quantum physics fulfil this principle. The reason for presenting this short paper is to draw attention to a series of papers that have appeared during the last years, in which the author criticized the usual scheme of quantum theory (Heisenberg picture, Schrodinger picture, etc.) and presented a new foundation of the basic laws of quantum physics, obeying the “principle of fundamental covariance” (Einstein's covariance principle in space-time and covariance principle in Hilbert space of quantum operators and states) [1].