Showing papers on "Open quantum system published in 1967"
553 citations
276 citations
TL;DR: In this paper, the eigenvalues of finite translations are used for specifying a complete set of states in quantum mechanics and a derivation of these states is given and they are shown to be very useful in solid-state physics.
Abstract: Eigenvalues of finite translations are used for specifying a complete set of states in quantum mechanics. A derivation of these states is given and they are shown to be very useful in solid-state physics.
274 citations
01 Jan 1967
TL;DR: This thesis is that the observer, or better, the experimentalist, plays in quantum theory exactly the same role as in classical physics.
Abstract: This is an attempt to exorcize the ghost called “consciousness” or “the observer” from quantum mechanics, and to show that quantum mechanics is as “objective” a theory as, say, classical statistical mechanics. My thesis is that the observer, or better, the experimentalist, plays in quantum theory exactly the same role as in classical physics. His task is to test the theory.
204 citations
TL;DR: The divergent part of Z3−1 is (Z 3 −1 )div = α0 2π 2 3 + α 0 2π − 1 4 α02π 2 log M 2 m 2 to sixth order in the bare charge e0, in a model in which corrections to internal photon lines in the vacuum polarization tensor are neglected as discussed by the authors.
116 citations
TL;DR: In this article, a reformulation of the axiomatic basis of quantum mechanics with particular reference to the manner in which the usual algebraic structures arise from certain natural physical requirements is presented.
Abstract: We present a reformulation of the axiomatic basis of quantum mechanics with particular reference to the manner in which the usual algebraic structures arise from certain natural physical requirements. Care is taken to distinguish between features of physical significance and those introduced for mathematical convenience. Our conclusion is that the usual algebraic structures cannot be significantly generalised without conflicting with our current experimental picture of processes occurring at the quantum level.
107 citations
95 citations
TL;DR: In this paper, a generalization of the current interpretation of quantum mechanics is proposed that would also include the case of incompatible observables, by taking advantage of the concept of complex probability measure.
Abstract: The empirical meaning of the simultaneity of measurement of several observables is carefully analyzed. General criteria sufficient to guarantee the internal consistency of a framework including simultaneous measurements of incompatible observables are put forward. The case is illustrated with the example of simultaneous measurements of position and momenta of particles in quantum mechanics. It is pointed out that, in general, the outcome of measurements of incompatible observables cannot be described statistically by means of the probability measures of mathematical statistics, which have primarily been introduced only with compatible observables in mind. The concept of complex probability measure is put forward. A generalization of the current interpretation of quantum mechanics is proposed that would also include the case of incompatible observables, by taking advantage of the concept of complex probability measure.
TL;DR: In this paper, an alternative theory for quantum theory is presented, employing three features which differ from the corresponding features of orthodox quantum theory: the state vector is never to be reduced, quantum theory only makes predictions about ensembles of identical experiments (not about individual experiments); and the measuring apparatus must always be included in the state vectors.
Abstract: An alternative calculational procedure for quantum theory is presented, employing three features which differ from the corresponding features of orthodox quantum theory. These are: (1) the state vector is never to be “reduced”; (2) quantum theory only makes predictions about ensembles of identical experiments (not about individual experiments); and (3) the measuring apparatus must always be included in the state vector. What is new about this alternative theory is the demonstration that Features 2 and 3 (which have hitherto been discussed separately) can be consistently combined to yield an interpretation of quantum theory which has the additional advantage of Feature 1. It is shown that alternative and orthodox theories yield identical predictions for any practical experiment. However, two classes of experiments (which are impractical) for which the orthodox and alternative theories yield different predictions are described. Therefore, it is, in principle, possible to decide which theory Nature has chosen to obey. It is concluded that there is no reason, based upon experimental evidence, for preferring one theory over the other.
TL;DR: In this paper, a brief discussion on the treatment of time-dependent phenomena in the non-relativistic quantum theory is given, and the phase problem is also discussed.
Abstract: Publisher Summary This chapter discusses quantum theory of time-dependent phenomena treated by the evolution operator technique. The purpose of this chapter is to give a brief discussion on the treatment of time-dependent phenomena in the non-relativistic quantum theory. In many of the applications, the theory has been quite successful and has led to results in complete agreement with experimental experience, but there are still certain difficulties connected with the concept of a complex wave function and particularly the evaluation of its phase. In the formula for time evolution , it may be possible to calculate the evolution operator but considerably more difficult to determine the wave function for the initial state. The phase problem is also discussed. The problem of the behavior of many-particle system under the influence of an outer electromagnetic field can be treated in principle, but it is more difficult to study the interaction between a system of matter waves and their own electromagnetic field. The problem of the self-interactions leads to divergence difficulties in both the non-relativistic and relativistic formulations of quantum theory, and the nature of the elementary particles themselves is still completely unknown.
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01 Jan 1967TL;DR: In this article, the effects of non-gauge-invariant potentials in quantum field theory are analyzed. But the effects are not necessarily quantum mechanical in nature and not necessarily related to the appearance of nongauges in the formulation of the theory.
TL;DR: In this article, it was shown that for a pure Fock state, the photoelectric counting distribution is binomial, and the counting fluctuations are less than those characteristic of a pure coherent state.
01 Jun 1967
TL;DR: In this paper, an extension of the procedure of Edwards and Sherrington for expanding in terms of correlations about the state of maximal quantum randomness is applied to the coupled system to give the density correltions and excitations as well as the corresponding single-particle quantities.
Abstract: In a discussion of the quantum dynamics of a non-relativistic many-particle system it is shown how a two-body interaction, quartic in the field operators, may be replaced by an interaction with an auxliary density-like field. An extension of the procedure of Edwards and Sherrington for expanding in terms of correlations about the state of maximal quantum randomness is applied to the coupled system to give the density correltions and excitations as well as the corresponding single-particle quantities. As an example, an explicit expression for the density excitations is obtained in terms of the quasi-particle energies, for the case in which quasi-particles exist as well-defined modes of single-particle excitation.
TL;DR: In this paper, a formulation of the measuring process is given, which allows an "objective" interpretation, starting from the unitary time transformation of the states of the measured systemS and the measuring deviceM, it is shown that after appropriate specification of the interaction HamiltonianHint between S and M and the macroscopic structure of M, the statistical operatorW of S+M approximately develops into the mixture, which is desired as result of the measurement process.
Abstract: After a short review of the present situation of the quantum theory of measurement, a formulation of the measuring process is given, which allows an “objective” interpretation. Starting from the unitary time transformation of the states of the measured systemS and the measuring deviceM, it is shown that after appropriate specification of the interaction HamiltonianHint betweenS andM and the macroscopic structure ofM, the statistical operatorW ofS+M approximately develops into the mixture, which is desired as result of the measuring process. During the process the interference terms practically vanish in the sense of weak operator convergence, while on the other hand their Hilbert-Schmidt norm remains constant.
TL;DR: In this article, a formalism of probability operators which generalizes the notion of density operator is introduced into the theory of noisy quantum systems and the Markov property and the connexion between Heisenberg and Schrodinger picture for systems undergoing an irreversible change are discussed in detail.
Abstract: A formalism of probability operators which generalizes the notion of density operator is introduced into the theory of noisy quantum systems. The Markov property and the connexion between Heisenberg and Schrodinger picture for systems undergoing an irreversible change are discussed in detail. The probability-operator treatment of noise is related to the Langevin method discussed byLax through a generalized Einstein-relation. The master equation for the quantum mechanical oscillator with linear damping is written down in a Fokker-Planck-type approximation. By means of the Einstein-relation the coefficients in the Fokker-Planck-equation are related to the parameters in the phenomenological equations.