Journal ArticleDOI
Who is afraid of nonhermitian operators? A quantum description of angle and phase
TLDR
In this article, the authors propose an unduly restricted framework for the theoretical description of quantum properties; non-hermitian operators, for instance unitary but also non-normal ones, may be acceptable as well if the projectors onto their eigenstates allow for a resolution of the identity operator, so as to preserve the probabilistic interpretation of the Hilbert space formalism.About:
This article is published in Annals of Physics.The article was published on 1976-09-24. It has received 161 citations till now. The article focuses on the topics: Ladder operator & Displacement operator.read more
Citations
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Journal ArticleDOI
Quantum metrology
TL;DR: It is proved that the typical quantum precision enhancement is of the order of the square root of the number of times the system is sampled, and it is pointed out the different strategies that permit one to attain this bound.
Journal ArticleDOI
Phase properties of the quantized single-mode electromagnetic field.
David T. Pegg,Stephen M. Barnett +1 more
TL;DR: This paper investigates the properties of a Hermitian phase operator which follows directly and uniquely from the form of the phase states in this space and finds them to be well behaved.
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On the Hermitian Optical Phase Operator
Stephen M. Barnett,David T. Pegg +1 more
TL;DR: In this paper, it was shown that the number-phase commutator differs from that originally postulated by Dirac and this difference allows consistent use of the commutators for inherently quantum states.
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Quantum gravity, shadow states and quantum mechanics
Abhay Ashtekar,Abhay Ashtekar,Stephen Fairhurst,Stephen Fairhurst,Stephen Fairhurst,Joshua L. Willis +5 more
TL;DR: In this article, the authors illustrate the conceptual problems and their solutions through a toy model: quantum mechanics of a point particle, which can also serve as a simple introduction to many of the ideas and constructions underlying quantum geometry.
References
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Journal ArticleDOI
Phase and Angle Variables in Quantum Mechanics
TL;DR: In this paper, a detailed analysis of the three-dimensional harmonic oscillator excited in coherent states is given, with special attention to the uncertainty relations and the transition to the classical limit.
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Phase of a Microscopic Electromagnetic Field and Its Measurement
TL;DR: In this paper, a novel approach to the quantum mechanical description of phase properties of a one-mode low-intensity radiation field is presented, based upon the correspondence between Glauber states and classical waves of fixed phase ϕ and amplitude a, and, in contrast to the conventional quantum mechanical phase concepts, allows to make contact between certain operators corresponding to the classical quantities exp {imφ} (m = ± 1, ± 2, …) and realistic measurements.
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Some Mathematical Properties of Oscillator Phase Operators
TL;DR: In this article, a general definition of cosine and sine operators for harmonic oscillator phase is proposed and its consequences examined, and an important feature of the spectral analysis is the ''chain sequence'' condition which ensures that C and S have unit norm.
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Oscillator phase states, thermal equilibrium and group representations
TL;DR: In this paper, the eigenstates of the annihilation type operator U = C + iS, where C and S are the cosine and sine operators for harmonic oscillator phase, are shown to be closely related to thermal equilibrium states of the oscillator and to provide a new interpretation of the thermal equilibrium density operator.
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Phase measurement of a microscopic radiation field
H. Gerhardt,U. Büchler,G. Litfin +2 more
TL;DR: In this paper, the phase measurement of a radiation field of only a few photons is presented, and the experimental results demonstrate that the phase of a microscopic radiation field is an observable and that a measurement system for the phase operator exists.