TEMPORAL QUANTUM FUNCTIONALS

© Oleg O. Feygin

Contact to the author: tor@3s.kharkov.ua

Reinterpretation of quantum-theoretical fashions based on discrete-temporal application principles of microscopic objects description contains a gang of reduction procedures, making processes spatially - time localization [1-5]. Thus, the kettle-integrated analysis of various variants of continuum structurization is used. It is necessary to precede the further development of quantum-theoretical models to operational representation for the basic discrete chronodynamic concepts.

The harmonic representation of microscopic objects psi-functions, in a quantum mechanics, with the subsequent coordinate differentiation, as is known, gives in the operational equation:

p*(q) ψ = p ψ, p*(q) = - ih/2π d/dq, (1)

where ð* - the functional representing dynamic variable ð(q). From the equation (1) it is visible, that consecutive application of the functional ð* to a psi-function gives its product on initial dynamic variable. The received effect shows, that the viewed psi-function features states in which making dynamic variable have quite particular values:

p*[q(x)] ψ[q(x)] = p(x) ψ(x), p*[q(y)] ψ[q(x)] = 0, ψ(x) = 0, p*[q(z)] ψ[q(x)] = 0, ψ(x) = 0,

p[q(x)] = p[p(x), 0, 0]. (2)

Consecutive of chronophysical reinterpretation relations (1) and (2), gives to

p*(q) = - i const h(e) h(t) d/dq, - i const h(e) dψ/dq = e*(q) ψ, - i const h(t) dψ/dq = t*(q) ψ, (3)

where h(e), h(t) – temporal-energy components of quantum; e*(q), t*(q) - temporal-energy functionals. At localization of a microscopic object in restricted area of space, the psi-function features a state in which the impulse has no precise value. In this case, the wave function is an undular package, everyone making which answers particular value chronoquantum numbers and defines a time determinations [1, 2]. Hence, such wave function (3) is an eigenfunction the functional (2) and represents a plane wave in subspace of events:

t*(q) ψ(t) = t(i) ψ(t), ψ(t) = S c(i) ψ(i), (4)

where c - characterizes in a complex view the relative statistical weight embodying taken together undular package. Accordingly, the probability of a microscopic object presence in some temporal shell t(i) will be equal to a quadrate of relevant amplitude module or product in a complex the conjugate quantities:

P[t(i)] = ψ(t) ψ*(t). (5)

More evidently the given equivalent first blanket chronophysical principle looks in labels of Dirac:

< t(i) | t(q) >. (6)

Similarly, the second blanket principle of a quantum mechanics is stated as an additively of complete probability amplitude localizations quantity to the total probability amplitudes of the next time shells:

< t(i) | t(q) > = < t(i-n) | t(q) > + … + < t(i+n) | t(q) >, (7)

where n - an iterative sequence next time shells. For correct determination, it is necessary for invariant localization of composition probability amplitude of process to formulate the third blanket principle quantum chronodynamic:

< t(i) | t(q) > = < t(i-1) | t(q) > < t(i+1) | t(q) >, (8)

I.e. the probability amplitude of localization on the allocated time shell may be submitted as product of nearest next shells probability amplitudes. In view of a relation (8), equality (7) may be submitted as:

< t(t) | t(q) > = < t(i-n-1) | t(q) > < t(i-n+1) | t(q) > + … + < t(i+n-1) | t(q) > < t(i+n+1) | t(q) >. (9)

Thus, the analysis of build-up chronoquantum functionals temporal legitimacies allows formulating analogs of three basic blanket principles of a quantum mechanics for composition probability amplitudes localizations on the relevant time shells.

REFERENCES

1. Feygin O.O. Discrete-Temporal Model of Universe // SciTecLibrary.com.2003.- http://www.sciteclibrary.ru/eng/catalog/pages/5159.html

2. Feygin O.O. Discrete Principles of Quantum Chronodynamic // Ibid.- http://www.sciteclibrary.ru/eng/catalog/pages/5200.html

3. Feygin O.O. Quantum-Theoretical Chrono-Discretization // Ibid.- http://www.sciteclibrary.ru/eng/catalog/pages/5201.html

4. Feygin O.O. Cosmological Principles of Quantum Chronophysics // Ibid.- http://www.sciteclibrary.ru/eng/catalog/pages/5296.html

5. Feygin O.O. Chronodynamic Reinterpretation of Planck’s Lengths // Ibid.- http://www.sciteclibrary.ru/eng/catalog/pages/5348.html

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