Quantum-mechanical stability of solitons and the correspondence principle

1993 ◽  
Vol 48 (3) ◽  
pp. 2361-2369 ◽  
Author(s):  
F. X. Kärtner ◽  
H. A. Haus
Keyword(s):  
Correspondence Principle ◽  
Mechanical Stability ◽  
Quantum Mechanical

scholarly journals IMPLICATIONS OF A QUANTUM MECHANICAL TREATMENT OF THE UNIVERSE

1998 ◽  
Vol 13 (05) ◽  
pp. 347-351 ◽  
Author(s):  
MURAT ÖZER
Keyword(s):  
Quantum Mechanics ◽  
Wave Packet ◽  
Early Universe ◽  
Mechanical Treatment ◽  
Correspondence Principle ◽  
Scale Factor ◽  
Quantum Mechanical ◽  
Quantum Mechanical Treatment ◽  
The Standard Model ◽  
The Universe

We attempt to treat the very early Universe according to quantum mechanics. Identifying the scale factor of the Universe with the width of the wave packet associated with it, we show that there cannot be an initial singularity and that the Universe expands. Invoking the correspondence principle, we obtain the scale factor of the Universe and demonstrate that the causality problem of the standard model is solved.

scholarly journals Quantum-mechanical stability of fermion–soliton systems

2004 ◽  
Vol 596 (1-2) ◽  
pp. 1-7 ◽  
Author(s):  
Narendra Sahu ◽  
Urjit A Yajnik
Keyword(s):  
Mechanical Stability ◽  
Quantum Mechanical

scholarly journals Energy spectra of electrons emitted from laser irradiated low-density gas and the correspondence principle of electromagnetic interaction

1995 ◽  
Vol 13 (1) ◽  
pp. 71-81 ◽  
Author(s):  
B.W. Boreham ◽  
H. Hora ◽  
H. Hora
Keyword(s):  
Correspondence Principle ◽  
Electromagnetic Interaction ◽  
Energy Spectra ◽  
Quantum Mechanical ◽  
Low Density ◽  
Mechanical Interaction

It is expected (Hora & Handel 1987) that the energy spectra of electrons emitted from laserirradiated atoms in low-density gases would be fundamentally different for laser intensities above and below the threshold of a correspondence principle. Below such a threshold, the emission is a quantum mechanical interaction while, in contrast, above the threshold it is a classical process. Both of our earlier experiments (Boreham & Hora 1979; Boreham & Luther-Davies 1979) and those of several others, including some very recent results (Monot et al. 1993) confirm—after some controversy—the existence of such a correspondence principle. Details are discussed.

Transition metal intermetallics: Structure maps based on quantum mechanical stability

2005 ◽  
Vol 178 (4) ◽  
pp. 1269-1283 ◽  
Author(s):  
Peter Michael Clark ◽  
Stephen Lee ◽  
Daniel C. Fredrickson
Keyword(s):  
Transition Metal ◽  
Mechanical Stability ◽  
Quantum Mechanical

scholarly journals IRROTATIONAL MOMENTUM FLUCTUATIONS CONDITIONING THE QUANTUM NATURE OF PHYSICAL PROCESSES

2006 ◽  
Vol 21 (26) ◽  
pp. 5299-5316
Author(s):  
STEPHAN I. TZENOV
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Correspondence Principle ◽  
Quantum Mechanical ◽  
Physical Processes ◽  
Expectation Values ◽  
Heisenberg Uncertainty Principle ◽  
Quantum Formalism ◽  
Classical Statistical Mechanics ◽  
Heisenberg Uncertainty

Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt, so that the quantum mechanical framework resembles to a large extent that of the classical statistical mechanics and hydrodynamics. The main assumption used here is the existence of a random irrotational component in the classical momentum. Various basic elements of the quantum formalism (calculation of expectation values, the Heisenberg uncertainty principle, the correspondence principle) are recovered by applying traditional techniques, borrowed from classical statistical mechanics.

Classical Statistics as a Limiting Case of Quantum Statistics

1967 ◽  
Vol 22 (9) ◽  
pp. 1333-1336 ◽  
Author(s):  
Wolfgang Kundt
Keyword(s):  
Correspondence Principle ◽  
Canonical Quantization ◽  
The Other ◽  
Quantum Mechanical ◽  
Position Space ◽  
General Validity ◽  
Coordinate Change ◽  
Hilbert Space Operators ◽  
Classical Statistics ◽  
Limiting Case

The scope of validity of the quantum mechanical correspondence principle is discussed: for what classes of HAMILTON functions does canonical quantization give rise to a quantum theory whose equilibrium predictions tend towards the classical ones in the limit of large energies? As the rule for canonical quantization we adopt the WEYL—WIGNER map (of real phase space functions onto selfadjoint HILBERT space operators) which appears to be the simplest that guarantees commutability of quantization with continuous coordinate change in position space. Counterexamples show that there is no general validity of a correspondence principle. On the other hand, such a principle is known to hold for all physically reasonable cases.

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