Geometry of a quantal system

1981 ◽  
Vol 19 (1) ◽  
pp. 83-93 ◽  
Author(s):  
Máximo García-Sucre ◽  
Mario Bunge
Keyword(s):  
Quantal System

Dynamics of a quantal system

1994 ◽  
Vol 577 (3-4) ◽  
pp. 813-828 ◽  
Author(s):  
V.N. Kondratyev ◽  
A. Smerzi ◽  
A. Bonasera
Keyword(s):  
Quantal System

Close-coupled calculations of transport cross-sections for a highly quantal system

1987 ◽  
Vol 62 (2) ◽  
pp. 397-409 ◽  
Author(s):  
G.C. Maitland ◽  
M. Mustafa ◽  
W.A. Wakeham
Keyword(s):  
Cross Sections ◽  
Quantal System

Classical limit of relativistic quantal system with attractive Coulomb interaction

Pramana ◽  
1991 ◽  
Vol 36 (3) ◽  
pp. 271-288
Author(s):  
Swagata Nandi ◽  
C S Shastry
Keyword(s):  
Coulomb Interaction ◽  
Classical Limit ◽  
Quantal System

Minimal Uncertainty in Quantal System Obeying the su(2)-Algebra

1992 ◽  
Vol 88 (4) ◽  
pp. 711-718 ◽  
Author(s):  
M. Yamamura ◽  
A. Kuriyama
Keyword(s):  
Quantal System

Quantal phase factors accompanying adiabatic changes

1984 ◽  
Vol 392 (1802) ◽  
pp. 45-57 ◽  
Keyword(s):  
Phase Factor ◽  
Symmetric Matrices ◽  
Sign Reversal ◽  
Dynamical Phase ◽  
Geometrical Phase ◽  
Sign Change ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Special Case ◽  
Quantal System

A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar dynamical phase factor. An explicit general formula for γ(C) is derived in terms of the spectrum and eigenstates of Ĥ(R) over a surface spanning C. If C lies near a degeneracy of Ĥ, γ(C) takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy. As an illustration γ(C) is calculated for spinning particles in slowly-changing magnetic fields; although the sign reversal of spinors on rotation is a special case, the effect is predicted to occur for bosons as well as fermions, and a method for observing it is proposed. It is shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor.

scholarly journals Incompatible Variables and “Quantal” Phenomena in Psychology

2011 ◽  
Vol 127 (1) ◽  
pp. 18-27
Author(s):  
ROGER A. HEGSTROM ◽  
GWEN ADSHEAD
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Theoretical Model ◽  
Cognitive Therapy ◽  
Experimental Testing ◽  
Standard Theory ◽  
Theoretical Treatment ◽  
Modern Psychology ◽  
Simple Theoretical Model ◽  
Quantal System

Abstract Mindfulness-based cognitive therapy (MBCT) is an area of modern psychology that provides a successful method for preventing the recurrence of depression. The standard theory of MBCT may be interpreted in terms of a simple theoretical model that employs incompatible variables as its fundamental observable quantities. Although the MBCT theory is not related to or derived from quantum theory, the existence of incompatible variables results in “quantal” phenomena, such as interference and the uncertainty principle, which have been widely believed to occur only as a consequence of the laws of quantum mechanics. The predictions of the model are subject to experimental testing and at present the model agrees with all published clinical data. To our knowledge, this work is the first quantitative theoretical treatment of a natural non-quantal system possessing incompatible variables. It confirms the intuition of Bohr and Heisenberg that incompatible variables may exist in human psychology.

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