scholarly journals Accidental degeneracy in a simple quantum system: A new symmetry group for a particle in an impenetrable square-well potential

1997 ◽  
Vol 65 (11) ◽  
pp. 1087-1094 ◽  
Author(s):  
F. Leyvraz ◽  
A. Frank ◽  
R. Lemus ◽  
M. V. Andrés
Keyword(s):  
Quantum System ◽  
Symmetry Group ◽  
System A ◽  
Simple Quantum ◽  
Accidental Degeneracy ◽  
Square Well

Local and nonlocal approximation for a simple quantum system

2001 ◽  
Vol 114 (10) ◽  
pp. 4386 ◽  
Author(s):  
M. A. Palenberg ◽  
R. J. Silbey ◽  
C. Warns ◽  
P. Reineker
Keyword(s):  
Quantum System ◽  
Simple Quantum

scholarly journals Period and toroidal knot mosaics

2017 ◽  
Vol 26 (05) ◽  
pp. 1750031 ◽  
Author(s):  
Seungsang Oh ◽  
Kyungpyo Hong ◽  
Ho Lee ◽  
Hwa Jeong Lee ◽  
Mi Jeong Yeon
Keyword(s):  
Quantum System ◽  
Prime Number ◽  
Growth Rates ◽  
Exact Enumeration ◽  
Common Features ◽  
System A ◽  
Number Formula ◽  
And Mathematics ◽  
Definition Of ◽  
Positive Integers

Knot mosaic theory was introduced by Lomonaco and Kauffman in the paper on ‘Quantum knots and mosaics’ to give a precise and workable definition of quantum knots, intended to represent an actual physical quantum system. A knot [Formula: see text]-mosaic is an [Formula: see text] matrix whose entries are eleven mosaic tiles, representing a knot or a link by adjoining properly. In this paper, we introduce two variants of knot mosaics: period knot mosaics and toroidal knot mosaics, which are common features in physics and mathematics. We present an algorithm producing the exact enumeration of period knot [Formula: see text]-mosaics for any positive integers [Formula: see text] and [Formula: see text], toroidal knot [Formula: see text]-mosaics for co-prime integers [Formula: see text] and [Formula: see text], and furthermore toroidal knot [Formula: see text]-mosaics for a prime number [Formula: see text]. We also analyze the asymptotics of the growth rates of their cardinality.

EXACT CANONICALLY CONJUGATE MOMENTA APPROACH TO AN SU(N) QUANTUM SYSTEM

1998 ◽  
Vol 13 (32) ◽  
pp. 5535-5556 ◽  
Author(s):  
SEIYA NISHIYAMA
Keyword(s):  
Quantum System ◽  
Natural Extension ◽  
Integral Equation Method ◽  
Collective Variables ◽  
Canonical Variables ◽  
System A ◽  
Symmetric Quantum ◽  
Collective Hamiltonian ◽  
Field Formalism ◽  
Derivatives Of

The collective field formalism by Jevicki and Sakita is a useful approach to the problem of treating general planar diagrams involved in an SU (N) symmetric quantum system. To approach this problem, standing on the Tomonaga spirit we also previously developed a collective description of an SU (N) symmetric Hamiltonian. However, this description has the following difficulties: (i) Collective momenta associated with the time derivatives of collective variables are not exact canonically conjugate to the collective variables; (ii) The collective momenta are not independent of each other. We propose exact canonically conjugate momenta to the collective variables with the aid of the integral equation method developed by Sunakawa et al. A set of exact canonical variables which are derived by the first quantized language is regarded as a natural extension of the Sunakawa et al.'s to the case for the SU (N) symmetric quantum system. A collective Hamiltonian is represented in terms of the exact canonical variables up to the order of [Formula: see text].

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