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 non-relativistic quantum mechanics; and (ii) for photons (i.e., in first-quantization quantum electrodynamics).
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 non-relativistic quantum mechanics; and (ii) for photons (i.e., in first-quantization quantum electrodynamics).
Some new results are presented and recent developments are reviewed on the study of Time in quantum physics 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-self-adjoint) operator for Time which appears: (i) for particles, in ordinary nonrelativistic quantum mechanics; and (ii) for photons (i.e. in first-quantization quantum electrodynamics). In conclusion, various recent and possible future applications of the time quantum analysis for tunnelling processes, nuclear collisions and systems with (quasi)discrete energy spectra are indicated.
Recent developments are reviewed and some new results are presented in the study of time in quantum mechanics and quantum electrodynamics as an observable, canonically conjugate to energy. This paper deals with the maximal Hermitian (but nonself‐adjoint) operator for time which appears in nonrelativistic quantum mechanics and in quantum electrodynamics for systems with continuous energy spectra and also, briefly, with the four‐momentum and four‐position operators, for relativistic spin‐zero particles. Two measures of averaging over time and connection between them are analyzed. The results of the study of time as a quantum observable in the cases of the discrete energy spectra are also presented, and in this case the quasi‐self‐adjoint time operator appears. Then, the general foundations of time analysis of quantum processes (collisions and decays) are developed on the base of time operator with the proper measures of averaging over time. Finally, some applications of time analysis of quantum processes (concretely, tunneling phenomena and nuclear processes) are reviewed.
Aim of this paper is to show the possible significance, and usefulness, of various non-self-adjoint operators for suitable Observables in non-relativistic and relativistic quantum mechanics, and in quantum electrodynamics.
More specifically, this work starts dealing with: (i) the maximal hermitian (but not selfadjoint) Time operator in non-relativistic quantum mechanics and in quantum electrodynamics; and with: (ii) the problem of the four-position and four-momentum operators, each one with its hermitian and anti-hermitian parts, for relativistic spin-zero particles. Afterwards, other physically important applications of non-selfadjoint (and even non-hermitian) operators are discussed: in particular, (iii) we reanalyze in detail the interesting possibility of associating quasi-hermitian Hamiltonians with (decaying) unstable states in nuclear physics. Finally, we briefly mention the cases of quantum dissipation, as well as of the nuclear optical potential.
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, with the introduction of Time and Space operators; and with (iii) the problem of the four-position and four-momentum 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 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 chapter 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]. PACS numbers: 03.65.Ta; 03.65.-w; 03.65.Pm; 03.70.+k; 03.65.Xp; 03.65.Yz; 11.10.St; 11.10.-z; 11.90.+t; 02.00.00; 03.00.00; 24.10.Ht; 03.65.Yz; 21.60.-u; 11.10.Ef; 03.65.Fd; 02.40.Dr; 98.80.Jk. Keywords: time operator, space-time operator, non-selfadjoint operators, non-hermitian operators, bilinear operators, time operator for discrete energy spectra, time-energy uncertainty relations, Klein-Gordon equation, chronon, quantum dissipation, decoherence, nuclear optical model, cosmology, projective relativity.
The aim of this paper is to show the possible significance, and usefulness, of various non-self-adjoint operators for suitable Observables in nonrelativistic and relativistic quantum mechanics, and in quantum electrodynamics. More specifically, this work deals with: (i) the maximal Hermitian (but not self-adjoint) time operator in nonrelativistic quantum mechanics and in quantum electrodynamics; (ii) the problem of the four-position and four-momentum operators, each one with its Hermitian and anti-Hermitian parts, for relativistic spin-zero particles. Afterwards, other physically important applications of non-self-adjoint (and even non-Hermitian) operators are discussed: in particular, (iii) we reanalyze in detail the interesting possibility of associating quasi-Hermitian Hamiltonians with (decaying) unstable states in nuclear physics. Finally, we briefly mention the cases of quantum dissipation, as well as of the nuclear optical potential.
The aim of this paper is to show the importance and applicability of non-self-adjoint operators for description of observables both in relativistic and nonrelativistic quantum mechanics, as well as in quantum electrodynamics. The paper considers (i) a maximally Hermitian (but non-self-adjoint) time operator in nonrelativistic quantum mechanics and in quantum electrodynamics and (ii) the problem of defining the four-dimensional coordinate and momentum operators describing relativistic particles with zero spin (each of these operators contains both Hermitian and anti-Hermitian parts). Some other applications of non-selfadjoint and non-Hermitian operators in physics are analyzed as well. The paper ends with an analysis of a few cases of T -non-invariant interactions, including quantum dissipation and nuclear optical potentials.