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Titolo:
NON-LIPSCHITZ APPROACH TO QUANTUM-MECHANICS
Autore:
ZAK M;
Indirizzi:
CALTECH,JET PROP LAB,CTR SPACE MICROELECT TECHNOL,4800 OAK GROVE DR PASADENA CA 91109
Titolo Testata:
Chaos, solitons and fractals
fascicolo: 7, volume: 9, anno: 1998,
pagine: 1183 - 1198
SICI:
0960-0779(1998)9:7<1183:NATQ>2.0.ZU;2-O
Fonte:
ISI
Lingua:
ENG
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
CompuMath Citation Index
CompuMath Citation Index
Science Citation Index Expanded
Science Citation Index Expanded
Science Citation Index Expanded
Citazioni:
9
Recensione:
Indirizzi per estratti:
Citazione:
M. Zak, "NON-LIPSCHITZ APPROACH TO QUANTUM-MECHANICS", Chaos, solitons and fractals, 9(7), 1998, pp. 1183-1198

Abstract

An attempt to reconcile quantum mechanics with Newton's laws represented by the non-Lipschitz formalism has been made. As a proof-of-concept, a line of equally spaced atoms was studied. It appeared that enforcement of atom incompressibility required relaxation of the Lipschitz condition at the points of contact. This, in turn, led to fractional powers and discreteness of values of the basic parameters including energy and action, and finally, to the uncertainty relationship between positions and velocities. In addition to that, the relaxation of the Lipschitz condition caused instability of velocity with respect to small changes of the atom position, and that introduced an element of randomness in the system behavior. It was shown that the only model for the probability evolution which incorporates all the new properties of themotions is the Schrodinger equation. This means that quantum mechanics can be derived from Newton's laws if an unnecessary mathematical restriction-the Lipschitz condition-is removed from the mathematical formalism. Non-local properties of the model, as well as spin-effects and relativistic corrections are discussed. (C) 1998 Elsevier Science Ltd. All rights reserved.

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Documento generato il 09/08/20 alle ore 23:33:13