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From Quantum Mechanics to Quantum Field Theory: The Hopf route
Quantum Mechanics Quantum Field Theory
2010/11/9
We show that the combinatorial numbers known as {\em Bell numbers} are generic in quantum physics. This is because they arise in the procedure known as {\em Normal ordering} of bosons, a procedure wh...
We first review the spectrum of the Laplacian operator on a general Laakso Space before considering modified Hamiltonians for the infinite square well, parabola, and Coulomb potentials. Additionally,...
We study the tunneling through delta and double delta potentials in fractional quantum mechanics. After solving the fractional Schr\"odinger equation for these potentials, we calculate the correspondi...
On the classical limit of quantum mechanics and the threat of fundamental graininess and chaos to the correspondence principle
classical limit of quantum mechanics threat of fundamental graininess correspondence principle
2010/12/16
The aim of this paper is to review the classical limit of Quantum
Mechanics and to precise the well known threat of chaos (and fundamental graininess) to the correspondence principle. We will introdu...
Complementarity in categorical quantum mechanics
Complementarity categorical quantum mechanics
2010/12/15
We relate notions of complementarity in three layers of quantum mechanics:(i) von Neumann algebras, (ii) Hilbert spaces, and (iii) orthomodular lattices.
A review of fundamentals and physical applications of fractional quantum mechanics has been presented.
Equations of motion in General Relativity and Quantum Mechanics
non-geodesic motion Dirac equation equations of motion Maxwell-Boltzmann distribution
2010/12/16
In a previous article a relationship was established between the linearized metrics of General Relativity associated with geodesics and the Dirac Equation of quantum mechanics.
Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics
supersymmetry separation of variables integrability solvability
2010/12/13
Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical sec...
S-linear operators in quantum mechanics and in economy
linear operator ]tempered distribution basis linear superposition linear independence system of coordinates
2009/1/9
In this paper we study the concept of S-linear operator and we show some of
its properties and applications to the foundations of Quantum Mechanics. This
new operators are a generalization of the li...
A generalization of Jaynes' principle: an information-theoretic interpretation of the minimum principles of quantum mechanics and gravitation
Jaynes' principle information-theoretic interpretation minimum principles
2010/11/1
By considering the "kinetic-energy" term of the minimum principle for the Schr\"{o}dinger equation as a measure of information, that minimum principle is viewed as a statistical estimation procedure,...