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Quantum computation and simulation with cold ions  Jonathan Home
Quantum computation and simulation with cold ions Jonathan Home

From Last Time… Today Particle in a box or a
From Last Time… Today Particle in a box or a

... Reducing the box size reduces position uncertainty, but the momentum uncertainty goes up! ...
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... The electron jumps from one quantum state to another, changing its wavefunction everywhere. During the transition, we say that the electron is briefly in a superposition between the two states. Phys107 Fall 2006 ...
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Press Release Equivalence principle also valid for atoms

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Presentation - Turing Gateway to Mathematics

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Quantum Computing - Turing Gateway

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... where h~r1 , ~r2 , . . . ~rN | is a normalized N-particle position eigenstate. For simplicity we shall consider the case without spin. The generalization to particles with spin is straightforward, but note that in the text one uses the notation x̂ ≡ |~rστ i where σ is a spin and τ some other interna ...
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Slides1 - University of Guelph

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Group Theory - gozips.uakron.edu

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PDF

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Quantum group

In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebra with additional structure. In general, a quantum group is some kind of Hopf algebra. There is no single, all-encompassing definition, but instead a family of broadly similar objects.The term ""quantum group"" first appeared in the theory of quantum integrable systems, which was then formalized by Vladimir Drinfeld and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a `bicrossproduct' class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo.In Drinfeld's approach, quantum groups arise as Hopf algebras depending on an auxiliary parameter q or h, which become universal enveloping algebras of a certain Lie algebra, frequently semisimple or affine, when q = 1 or h = 0. Closely related are certain dual objects, also Hopf algebras and also called quantum groups, deforming the algebra of functions on the corresponding semisimple algebraic group or a compact Lie group.Just as groups often appear as symmetries, quantum groups act on many other mathematical objects and it has become fashionable to introduce the adjective quantum in such cases; for example there are quantum planes and quantum Grassmannians.
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