Amplitude and phase uncertainty relations

Louisell, W. H.

doi:10.1016/0031-9163(63)90442-6

Cited by 201 publications

(120 citation statements)

References 2 publications

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“…My curiosity on this point arose independently of your own, as I recall. (Also Louisell [21].) In any event, I think that my problem, or your remark, however perceptive and important towards motivating the solution, did not especially deserve reference.…”

Section: The Discovery Of Quantum Sin and Cos Operatorsmentioning

confidence: 99%

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Quantum phase and quantum phase operators: some physics and some history

Nieto

1993

Phys. Scr.

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After reviewing the role of phase in quantum mechanics, I discuss, with the aid of a number of unpublished documents, the development of quantum phase operators in the 1960's. Interwoven in the discussion are the critical physics questions of the field: Are there (unique) quantum phase operators and are there quantum systems which can determine their nature? I conclude with a critique of recent proposals which have shed new light on the problem.

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Section: The Discovery Of Quantum Sin and Cos Operatorsmentioning

confidence: 99%

“…Before discussing the role of Louisell in this field [21], I want, and will need, to bring up another question. Can one obtain discrete eigenvalues of the C and S operators in physical systems?…”

Section: Are There Discrete Quantized-phase Eigenvalues?mentioning

confidence: 99%

Quantum phase and quantum phase operators: some physics and some history

Nieto

1993

Phys. Scr.

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“…All of them must bow to the fact that no phase operator can be canonical with the number operatorn =â †â . This 'no-go' theorem was pointed out by Louisell [20] and follows directly by contradiction: If it were true that [φ,n] = i, then taking diagonal matrix elements of this equation with respect to the ground state |h 0 would imply that 0 = i.…”

Section: Matrix Elements: the Phase Anglementioning

confidence: 97%

Wavefunctions on phase space

Smith¹

2006

J. Phys. A: Math. Gen.

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Theories of , Harriman [6], and of Ban [11], in which phase space points (p,q) are used as configurational variables to formulate quantum mechanics are considered from the standpoint of a class of quantization schemes associating phase space functions with operators. The connection between these schemes and the theories given in [5] to [11] is made by means of augmented wave functions ψ (λ) σ (p, q; t), where λ = 0 corresponds to the ordering of Wigner and Weyl. For that case we use these functions to define a family of positive operator-valued measures for the phase angle of an harmonic oscillator.

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“…Louisell [5] first introduced the periodic operator function in defining a phase variable conjugate to the angular momentum. Carrauthers and Nieto [7] showed that one can define two Hermitian phase operators C and S corresponding to cosine and sine of the classical phase, respectively.…”

Section: Quantum Phase Operatorsmentioning

confidence: 99%

“…As far as quantum phase measurement and its theoretical interpretations are concerned, there are unresolved issues which need to be addressed, in particular in the context of emerging field of atom optics. For instance, a proper definition of 'quantum phase' of electromagnetic fields had remained a hotly debated topic in theoretical quantum physics for a long time [4,5,6,7,8]. Accurate determination of phase difference between two optical fields in the quantum domain remains an elusive task due to lack of theoretical understanding of quantum phases.…”

Section: Introductionmentioning

confidence: 99%

Unitary quantum phase operators for bosons and fermions: a model study on the quantum phases of interacting particles in a symmetric double-well potential

Das¹,

Ghosal²,

Gupta³

et al. 2013

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. We introduce unitary quantum phase operators for material particles. We carry out a model study on quantum phases of interacting bosons in a symmetric double-well potential in terms of unitary and commonly-used non-unitary phase operators and compare the results for different number of bosons. We find that the results for unitary quantum phase operators are significantly different from those for non-unitary ones especially in the case of low number of bosons. We introduce unitary operators corresponding to the quantum phase-difference between two single-particle states of fermions. As an application of fermionic phase operators, we study a simple model of a pair of interacting two-component fermions in a symmetric double-well potential. We also investigate quantum phase and number fluctuations to ascertain number-phase uncertainty in terms of unitary phase operators.

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Amplitude and phase uncertainty relations

Cited by 201 publications

References 2 publications

Quantum phase and quantum phase operators: some physics and some history

Quantum phase and quantum phase operators: some physics and some history

Wavefunctions on phase space

Unitary quantum phase operators for bosons and fermions: a model study on the quantum phases of interacting particles in a symmetric double-well potential

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