The punctual approximations to the extended-type position

Gallardo, J.A. García; Kálnay, A. J.; Stec, Boguslaw; Toledo, B. P.

doi:10.1007/bf02721624

Cited by 24 publications

(14 citation statements)

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“…It is noteworthy (Olkhovsky & Recami, 1968;1969) that, as we are going to see, operator (68a) is nothing but the usual Newton-Wigner operator, while (68b) can be interpreted (Gallardo et al, 1967b;Ka'lnay, 1966;Ka'lnay & Toledo, 1967;Olkhovsky et al, 1967;Olkhovsky & Recami, 1968;1969;Toller, 1999) as yielding the sizes of the localization-region (an ellipsoid) via its average values over the considered wave-packet. Let us underline that the previous formalism justifies from the mathematical point of view the treatment presented in papers like (Baldo & Recami, 1969;Gallardo et al, 1967b;Ka'lnay, 1966;Ka'lnay & Toledo, 1967;Olkhovsky et al, 1967;Recami, 1970). We can split (Olkhovsky & Recami, 1968;1969) the operatorẑ into two bilinear parts, as follows: (Baldo & Recami, 1969;Gallardo et al, 1967b;Ka'lnay, 1966;Ka'lnay & Toledo, 1967;Olkhovsky et al, 1967;Recami, 1970;Recami et al, 1983) space of wave packets.…”

Section: The Klein-gordon Case: Three-position Operatorsmentioning

confidence: 86%

“…Following, e.g., the ideas in Ref. (Gallardo et al, 1967b;Ka'lnay, 1966;Ka'lnay & Toledo, 1967;Olkhovsky et al, 1967), we are going to show that the mean values of the hermitian (selfadjoint) part ofẑ will yield a mean (point-like) position (Baldo & Recami, 1969;Recami, 1970), while the mean values of the anti-hermitian (anti-selfadjoint) part ofẑ will yield the sizes of the localization region (Olkhovsky & Recami, 1968;1969). Let us consider, e.g., the case of relativistic spin-zero particles, in natural units and with metric (+ − − −).…”

Section: The Klein-gordon Case: Three-position Operatorsmentioning

confidence: 99%

“…The position operator i ∇ p , is known to be actually non-hermitian, and may be in itself a good candidate for an extended-type position operator. To show this, we want to split (Gallardo et al, 1967b;Ka'lnay, 1966;Ka'lnay & Toledo, 1967;Olkhovsky et al, 1967) it into its hermitian and anti-hermitian (or skew-hermitian) parts. Consider, then, a vector space V of complex differentiable functions on a 3-dimensional phase-space (Recami et al, 1983) equipped with an inner product defined by…”

Section: The Klein-gordon Case: Three-position Operatorsmentioning

confidence: 99%

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On measurements in quantum mechanics

Waerden

1966

Z. Physik

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Section: The Klein-gordon Case: Three-position Operatorsmentioning

confidence: 86%

Section: The Klein-gordon Case: Three-position Operatorsmentioning

confidence: 99%

Section: The Klein-gordon Case: Three-position Operatorsmentioning

confidence: 99%

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On measurements in quantum mechanics

Waerden

1966

Z. Physik

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“…It is noteworthy [3,4] that, as we are going to see, operator (42a) is nothing but the usual Newton-Wigner operator, while (42b) can be interpreted [52][53][54][55][56]3,4,31] as yielding the sizes of the localization-region (an ellipsoid) via its average values over the considered wave-packet. Let us underline that the previous formalism justifies from the mathematical point of view the treatment presented in papers like [52][53][54][55][56][57][58].…”

Section: The Klein-gordon Case: Three-position Operatorsmentioning

confidence: 99%

On a Time–Space Operator (and other Non-Self-Adjoint Operators) for Observables in QM and QFT

Recami¹,

Zamboni‐Rached²,

Licata³

2016

Beyond Peaceful Coexistence

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Aim of this paper is trying to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non-relativistic and relativistic quantum mechanics, and in quantum electrodynamics: More specifically, this work starts dealing with: (i) the hermitian (but not selfadjoint) Time operator in non-relativistic quantum mechanics and in quantum electrodynamics; with (ii) idem, the introduction of Time and Space operators; and with (iii) the problem of the four-position and fourmomentum operators, each one with its hermitian and anti-hermitian parts, for relativistic spin-zero particles. Afterwards, other physical applications of non-selfadjoint (and even non-hermitian) operators are briefly discussed. We briefly mention how non-hermitian operators can indeed be used in physics [as it was done, elsewhere, for describing Unstable States]; and some considerations are added on the cases of the nuclear optical potential, of quantum dissipation, and in particular of an approach to the measurement problem in QM in terms of a chronon. This paper is largely based on work developed, along the years, in collaboration with V.S.Olkhovsky, and, in smaller parts, with P.Smrz, with R.H.A.Farias, and with S.P.Maydanyuk.

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“…[32][33][34][35][36][37][38][39][40][41]. Also, other relevant sectors of quantum mechanics and quantum field theory, including unstable-state decays, will be considered elsewhere.…”

Section: An Operator For Time In Quantum Physics For Non-relativisticmentioning

confidence: 99%

NEW DEVELOPMENTS IN THE STUDY OFTIMEAS A QUANTUM OBSERVABLE

Olkhovsky

Recami

2008

Int. J. Mod. Phys. B

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Some results are briefly reviewed and developments are presented on the study of Time in quantum mechanics as an observable, canonically conjugate to energy. Operators for the observable Time are investigated in particle and photon quantum theory. In particular, this paper deals with the hermitian (more precisely, maximal hermitian, but non-selfadjoint) operator for Time which appears: (i) for particles, in ordinary nonrelativistic quantum mechanics; and (ii) for photons (i.e., in first-quantization quantum electrodynamics).Keywords: Time and energy as canonically conjugated quantum observables; maximal heermition operator; time-energy uncertainty relation; mean time; continuous and discrete energy spectra.b Such a condition is enough for operator (1a), (1b) to be an hermitian (or, more precisely, "maximal hermitian") operator 7-11 (see also , according to Akhiezer & Glazman's terminology. 43 Let us explicitly notice that, anyway, this physically reasonable boundary condition E = 0 can be dispensed with, by having recourse to bi-linear operators, as shown by us in Appendix B. Int. J. Mod. Phys. B 2008.22:1877-1897. Downloaded from www.worldscientific.com by GEORGE WASHINGTON UNIVERSITY on 02/09/15. For personal use only.

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The punctual approximations to the extended-type position

Cited by 24 publications

References 10 publications

On measurements in quantum mechanics

On measurements in quantum mechanics

On a Time–Space Operator (and other Non-Self-Adjoint Operators) for Observables in QM and QFT

NEW DEVELOPMENTS IN THE STUDY OFTIMEAS A QUANTUM OBSERVABLE

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