Exact wave functions of an electron on a quasiperiodic lattice: Definition of an infinite‐dimensional Riemann theta function

1992 ◽  
Vol 33 (11) ◽  
pp. 3938-3947 ◽  
Author(s):  
Kazumoto Iguchi
Keyword(s):  
Theta Function ◽  
Wave Functions ◽  
Riemann Theta Function ◽  
Infinite Dimensional ◽  
Definition Of

scholarly journals Quasi-regularity in Optimization

1986 ◽  
Vol 41 (2) ◽  
pp. 188-192 ◽  
Author(s):  
Kung-Fu Ng ◽  
David Yost
Keyword(s):  
Banach Space ◽  
Lagrange Multiplier ◽  
Optimization Problems ◽  
General Situation ◽  
Lagrange Multiplier Rule ◽  
Infinite Dimensional ◽  
Space Setting ◽  
Multiplier Rule ◽  
Dimensional Version ◽  
Definition Of

AbstractThe notion of quasi-regularity, defined for optimization problems in Rn, is extended to the Banach space setting. Examples are given to show that our definition of quasi-regularity is more natural than several other possibilities in the general situation. An infinite dimensional version of the Lagrange multiplier rule is established.

White noise delta functions and infinite-dimensional Laplacians

2020 ◽  
pp. 2050028
Author(s):  
Luigi Accardi ◽  
Ai Hasegawa ◽  
Un Cig Ji ◽  
Kimiaki Saitô
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Time Derivative ◽  
Delta Function ◽  
Itô Formula ◽  
Ito Formula ◽  
Infinite Dimensional ◽  
Delta Functions ◽  
Definition Of ◽  
White Noise Distribution

In this paper, we introduce a new white noise delta function based on the Kubo–Yokoi delta function and an infinite-dimensional Brownian motion. We also give a white noise differential equation induced by the delta function through the Itô formula introducing a differential operator directed by the time derivative of the infinite-dimensional Brownian motion and an extension of the definition of the Volterra Laplacian. Moreover, we give an extension of the Itô formula for the white noise distribution of the infinite-dimensional Brownian motion.

EPR Elements of Physical Reality in Quantum Mechanics

1997 ◽  
Vol 12 (29) ◽  
pp. 5289-5303
Author(s):  
V. K. Thankappan ◽  
Ravi K. Menon
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Singlet State ◽  
Physical Reality ◽  
The State ◽  
Wave Functions ◽  
Definition Of

The concept of elements of physical reality (e.p.r.) in quantum mechanics as defined by Einstein, Podolsky and Rosen (EPR) is discussed in the context of the EPR–Bohm and the EPR–Bell experiments on a pair of spin 1/2 particles in the singlet state. It is argued that EPR's definition of e.p.r. is appropriate to the EPR–Bell experiment rather than to the EPR–Bohm experiment, and that Bohr's interpretation of e.p.r. is also consistent with such a viewpoint. It is shown that the observed correlation between the spins of the two particles in the EPR–Bell experiment is just a manifestation of the correlation that exists between the wave functions of the particles in the singlet state and a consequence of the fact that a Stern–Gerlach magnet does not change the state of a particle but only transforms its wave function into a representation defined by the axis of the magnet. As such, the correlation is suggested to be an affirmation of Einstein's concept of locality, and not an evidence for nonlocality.

scholarly journals TOWARDS A DEFINITION OF QUANTUM INTEGRABILITY

2009 ◽  
Vol 06 (01) ◽  
pp. 129-172 ◽  
Author(s):  
JESÚS CLEMENTE-GALLARDO ◽  
GIUSEPPE MARMO
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Degrees Of Freedom ◽  
Complete Integrability ◽  
Infinite Dimensional ◽  
Quantum Integrability ◽  
Classical Systems ◽  
Definition Of ◽  
Geometrical Formulation ◽  
Quantum Framework

We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to the quantum framework would not work because all infinite dimensional Hilbert spaces are unitarilly isomorphic and, as a consequence, it would not be easy to define degrees of freedom. We argue that a geometrical formulation of quantum mechanics might provide a way out.

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