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Polynomial Heisenberg algebras and Painleve
Polynomial Heisenberg algebras and Painleve

... contributions of this thesis in the area: a new Wronskian formula for the confluent SUSY transformation [Bermudez et al., 2012] and the application of SUSY QM to the inverted oscillator potential [Bermudez and Fernández, 2013b]. After that, we will present the definitions of the Heisenberg-Weyl alg ...
Lectures on the Geometry of Quantization
Lectures on the Geometry of Quantization

here
here

Ph125: Quantum Mechanics
Ph125: Quantum Mechanics

Quantum Measurement and Control
Quantum Measurement and Control

BORDISM: OLD AND NEW What follows are lecture notes from a
BORDISM: OLD AND NEW What follows are lecture notes from a

... element of νp , but there is no canonical basis independent of the coordinate system. However, any two such vectors are in the same component of νp \ {0}, which means that ν carries a canonical orientation. (We review orientations in Lecture 2.) thm:4 ...
QUANTUM STRUCTURES FOR LAGRANGIAN SUBMANIFOLDS
QUANTUM STRUCTURES FOR LAGRANGIAN SUBMANIFOLDS

... Let f : L → R be a Morse function on L and let ρ be a Riemannian metric on L so that the pair (f, ρ) is Morse-Smale. Fix also a generic almost complex structure J compatible with ω. It is well known that, under the above assumption of monotonicity, the Floer homology of the pair (L, L) is well defin ...
IMPRECISE MEASUREMENTS IN QUANTUM MECHANICS
IMPRECISE MEASUREMENTS IN QUANTUM MECHANICS

Quantum Theory, Groups and Representations: An Introduction (under construction) Peter Woit
Quantum Theory, Groups and Representations: An Introduction (under construction) Peter Woit

Lectures on Arithmetic Noncommutative Geometry Matilde Marcolli
Lectures on Arithmetic Noncommutative Geometry Matilde Marcolli

Decoherence and open quantum systems
Decoherence and open quantum systems



... relation E ≤ρ F , and due to the validity of transitivity of SD implication in B, E ≤ρ F follows. On ground of Proposition 2.4 we can define a poset structure in B/∼ρ . Definition 2.5. One has EB ≤ρ FB if for all E ∈ EB and for all F ∈ FB the relation E ≤ρ F is valid. Lemma 2.6 ...
Ph125: Quantum Mechanics
Ph125: Quantum Mechanics

... states; for example, if a classical particle only has access to classical state 1 with phase space coordinates (x1 , p1 ) and classical state 2 with (x2 , p2 ), the particle can only be in one or the other; there is no way to “combine” the two states. Another way of saying this is that quantum mecha ...
Metric gluing of Brownian and sqrt(8/3)-Liouville
Metric gluing of Brownian and sqrt(8/3)-Liouville

- City Research Online
- City Research Online

... have ExtiG (V, W ) = ExtiPol (V, W ), by [10], Section 4,(5). For G-modules V, W we shall often simply write Exti (V, W ) for ExtiG (V, W ), though occasionally write ExtiG (V, W ) or ExtiPol (V, W ), as appropriate, for emphasis. We shall also write simply Ext(V, W ) for Ext1G (V, W ). In the case ...
Download: PDF
Download: PDF

... h was a new constant called Planck’s constant, given by h  6.626 1034 J  s  4.136 1015 eV  s. This is the basis of the modern photomultiplier, a device that is capable of detecting individual particles of light, also known as photons. We aren’t really interested in the inner workings of a re ...
For screen - Mathematical Sciences Publishers
For screen - Mathematical Sciences Publishers

Bachelor Thesis - Institut für Analysis und Scientific Computing
Bachelor Thesis - Institut für Analysis und Scientific Computing

... Introduction and historical aspects Different forms of knots have been known since long ago. They had technical applications, like in shipping, or weaving. More interesting and in particular aesthetically pleasing were the mystic symbols in many cultures. Famous examples are the sign of the pythago ...
Quantum Information with Fermionic Gaussian States - Max
Quantum Information with Fermionic Gaussian States - Max

... Many models of high physical relevance are diagonalizable using Bogoliubov transformation. Let us mention for example Hubbard models or mean-field theory in the first approximation of BCS superconductivity theory. The ground state of quadratic Hamiltonian (2.11) that describe definite set of quasi-p ...
Aspects of quantum information theory
Aspects of quantum information theory

Quantum Nonlinear Optics in Lossy Coupled-Cavities in Photonic Crystal Slabs
Quantum Nonlinear Optics in Lossy Coupled-Cavities in Photonic Crystal Slabs

(Never) Mind your p`s and q`s: Von Neumann versus Jordan on the
(Never) Mind your p`s and q`s: Von Neumann versus Jordan on the

Quantum Measurement Theory
Quantum Measurement Theory

Daniel Adam Roberts - School of Natural Sciences
Daniel Adam Roberts - School of Natural Sciences

... In many of my papers, acknowledgments have been a space for sincere thanks, literal acknowledgments (of funding sources), and hidden jokes. This is made possible by the fact that in all of my papers, the acknowledgments have come at the end. In this work, we are instructed to do things sdrawkcab. It ...
REFLECTION POSITIVITY, RANK
REFLECTION POSITIVITY, RANK

... 2.2. Connection matrices of a graph parameter. A graph parameter is a function on finite graphs (invariant under graph isomorphism). We allow multiple edges in our graphs, but no loops. A graph parameter f is called multiplicative, if for the disjoint union G1 ∪G2 of two graphs G1 and G2 , we have f ...
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Compact operator on Hilbert space

In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite-rank operators in the uniform operator topology. As such, results from matrix theory can sometimes be extended to compact operators using similar arguments. In contrast, the study of general operators on infinite-dimensional spaces often requires a genuinely different approach.For example, the spectral theory of compact operators on Banach spaces takes a form that is very similar to the Jordan canonical form of matrices. In the context of Hilbert spaces, a square matrix is unitarily diagonalizable if and only if it is normal. A corresponding result holds for normal compact operators on Hilbert spaces. (More generally, the compactness assumption can be dropped. But, as stated above, the techniques used are less routine.)This article will discuss a few results for compact operators on Hilbert space, starting with general properties before considering subclasses of compact operators.
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