Degenerate discrete energy spectra and associated coherent states

2007 ◽  
Vol 48 (1) ◽  
pp. 012110 ◽  
Author(s):  
L. Dello Sbarba ◽  
V. Hussin
Keyword(s):  
Coherent States ◽  
Energy Spectra ◽  
Discrete Energy

scholarly journals TIME AS A QUANTUM OBSERVABLE

2007 ◽  
Vol 22 (28) ◽  
pp. 5063-5087 ◽  
Author(s):  
V. S. OLKHOVSKY ◽  
E. RECAMI
Keyword(s):  
Quantum Electrodynamics ◽  
Quantum Physics ◽  
Adjoint Operator ◽  
Energy Spectra ◽  
Discrete Energy ◽  
Nuclear Collisions ◽  
Quantum Analysis ◽  
Recent Developments ◽  
Time Quantum ◽  
Nonrelativistic Quantum Mechanics

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.

The time evolution of quantum systems with discrete energy spectra

1986 ◽  
Vol 64 (11) ◽  
pp. 1546-1550 ◽  
Author(s):  
A. I. Lupaşcu ◽  
I. M. Popescu
Keyword(s):  
Time Evolution ◽  
Quantum Systems ◽  
The State ◽  
Energy Spectra ◽  
Matrix Functions ◽  
Level Crossing ◽  
Discrete Energy ◽  
Nonexponential Decay

Using the method of matrix functions, we describe the time evolution of quantum systems with discrete energy spectra. The time evolution of the state vectors and expressions for the perturbed eigenfunctions and their associated projectors are obtained for an atom with n discrete levels. The particular cases n = 2 and n = 3 are presented; level crossing and nonexponential decay of coupled states are emphasized.

UNCERTAINTY RELATIONS FOR A DEFORMED OSCILLATOR

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1851-1859 ◽  
Author(s):  
JOSÉ RÉCAMIER ◽  
W. LUIS MOCHÁN ◽  
MARÍA GORAYEB ◽  
JOSÉ L. PAZ ◽  
ROCÍO JÁUREGUI
Keyword(s):  
Coherent States ◽  
Morse Potential ◽  
Temporal Evolution ◽  
Energy Spectra ◽  
Uncertainty Relations ◽  
Morse Oscillator ◽  
Algebraic Representation ◽  
Creation And Annihilation Operators ◽  
Deformed Oscillator ◽  
Minimum Uncertainty

We construct a deformed oscillator whose energy spectra is similar to that of a Morse potential. We obtain a convenient algebraic representation of the displacement and the momentum of a Morse oscillator by expanding them in terms of deformed creation and annihilation operators and we compute their average values between approximate coherent states of the deformed oscillator, and we compare them to the results obtained using the exact Morse coordinate and momenta. Finally we evaluate the temporal evolution of the dispersion (Δx)(Δp) and show that these states are not minimum uncertainty states.

scholarly journals Collective Electron-Positron Annihilation

1992 ◽  
Vol 128 ◽  
pp. 117-122
Author(s):  
A. A. Belyanin ◽  
V. V. Kocharovskii ◽  
Vl. V. Kocharovskii
Keyword(s):  
Positron Annihilation ◽  
Coherent Radiation ◽  
Energy Spectra ◽  
Relaxation Rates ◽  
Collisional Relaxation ◽  
Discrete Energy ◽  
Electron Positron Annihilation ◽  
Electron Positron

AbstractThe phenomenon of collective spontaneous annihilation of a magnetized electron-positron plasma is predicted. Like the superradiance in systems with discrete energy spectra, collective annihilation leads to the generation of powerful coherent radiation with the rate of this process considerably exceeding the spontaneous annihilation and collisional relaxation rates.

scholarly journals Coherent states of systems with pure continuous energy spectra

2021 ◽  
Vol 62 (6) ◽  
pp. 063510
Author(s):  
Zouhaïr Mouayn ◽  
Hashim A. Yamani
Keyword(s):  
Coherent States ◽  
Energy Spectra ◽  
Continuous Energy

scholarly journals Time as a Quantum Observable, Canonically Conjugated to Energy, and Foundations of Self-Consistent Time Analysis of Quantum Processes

2009 ◽  
Vol 2009 ◽  
pp. 1-83 ◽  
Author(s):  
V. S. Olkhovsky
Keyword(s):  
Quantum Mechanics ◽  
Quantum Electrodynamics ◽  
Adjoint Operator ◽  
Time Operator ◽  
Energy Spectra ◽  
Time Analysis ◽  
Quantum Processes ◽  
Discrete Energy ◽  
Quantum Observable ◽  
Over Time

Recent developments are reviewed and some new results are presented in the study oftimein quantum mechanics and quantum electrodynamics as an observable, canonically conjugate toenergy. 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.

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