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.

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.

NEW DEVELOPMENTS IN THE STUDY OFTIMEAS A QUANTUM OBSERVABLE

2008 ◽  
Vol 22 (12) ◽  
pp. 1877-1897 ◽  
Author(s):  
V. S. OLKHOVSKY ◽  
E. RECAMI
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Electrodynamics ◽  
Selfadjoint Operator ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
New Developments ◽  
Quantum Observable ◽  
Time In Quantum Mechanics

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).

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

Inequality, Exclusion, and Tolerance for Political Dissent in Latin America

2021 ◽  
pp. 001041402199716
Author(s):  
Jana Morgan ◽  
Nathan J. Kelly
Keyword(s):  
Latin America ◽  
Public Opinion ◽  
Social Inclusion ◽  
Political Tolerance ◽  
Time Analysis ◽  
Political Dissent ◽  
Structural Context ◽  
Democratic Rights ◽  
Over Time ◽  
Cross National

Although many countries meet electoral standards of democracy, often these regimes fail to promote social inclusion or meaningful representation. We argue that systems of exclusion have deleterious consequences for how people think about democracy, undermining tolerance for political dissent. Using cross-national public opinion data together with contextual measures of economic and political marginalization along ethnoracial lines, we evaluate the relationships between exclusion and political tolerance across Latin America. Over-time analysis in Bolivia further probes the mechanisms linking exclusion to intolerance. We find that tolerance of dissent is depressed where ethnoracial hierarchies are pronounced. We advance understanding of oft-unexplained society-level differences in political tolerance and emphasize the importance of the macro-structural context in shaping citizens’ commitments to basic democratic rights.

What Is Light, Really?

2011 ◽  
Author(s):  
Sönke Johnsen
Keyword(s):  
Quantum Mechanics ◽  
Physical Properties ◽  
Quantum Entanglement ◽  
Uncertainty Principle ◽  
Modern Theory ◽  
Discrete Energy ◽  
Wave Particle Duality ◽  
The World ◽  
Energy States

This concluding chapter explains that the modern theory of light falls within the field of quantum mechanics. At first glance, quantum mechanics does not seem that strange—its name is based on the fact that light comes in units and that electrons have discrete energy states. It also includes the uncertainty principle, which states that one cannot know certain pairs of physical properties with perfect precision. Moreover, quantum mechanics involves the wave-particle duality of photons. The chapter then explores two of the most unusual aspects of quantum mechanics: two-slit interference and quantum entanglement. Both violate the most fundamental notions about how the world works.

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