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MS-word - Table of Contents
MS-word - Table of Contents

... There are two combinations of the basic waves: electrons and positrons, which have opposite phase and spin rotation. Thus matter is constituted of two binary elements - like computer hardware Although the variety of molecules and materials populating the universe is enormous, the basic building bric ...
Quantum computation of scattering in scalar quantum field theories
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Electron-positron pair production in space- or time
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... The creation of electron-positron pairs from the vacuum by an external uniform electric field in spacetime was first studied by Sauter [1] as a quantum tunneling process. Heisenberg and Euler [2] extended his result by calculating an effective Lagrangian from the Dirac theory for electrons in a cons ...
Sections 4 - Columbia Physics
Sections 4 - Columbia Physics

... frame in which one of the two particles is not moving. Suppose that in the center of mass reference frame the two particles are initially moving along x with velocities v = ±0.8c. In the lab frame one particle has velocity v = 0 and the other particle has a velocity which is directed along negative ...
Broglie and Schrodinger Atomic Model
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... particle duality theory of matter, this was also with the help of research that Albert Einstein had found. Broglie’s hypothesis was “Any moving particle or object has an associated wave”. His discovery of wave mechanics which merged the physics of light and matter earned him the nobel prize. Informa ...
Quantum cryptography
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... • Many “protocols” have been developed for QKD each of which use nonorthogonal basis sets – E.g. BB84 which uses (H,V) and (+45,-45) polarization states of light – “Send and measure” with some classical communication resources – Final steps consist of a “classical” error correction and privacy ampli ...
Commun. Math. Phys. 227, 605 (2002).
Commun. Math. Phys. 227, 605 (2002).

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... states. In the experiment, to detect the action over distance, the spectral function A! can be measured by varying the detuning of the laser fields to the atomic transition   !L  !A [24,25], where !L is the frequency difference between the two laser fields for the two-photon Raman process, and ...
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Surrey seminar on CQP - School of Computing Science
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... Suppose that Alice continues with some behaviour, after sending the qubit to Bob. Alice(x:Qbit, q:^[Qbit], n:0..3) = {x *= n} . q![x] . Continue The type system of CQP guarantees that Continue does not refer to x. Technically: the fact that x is sent along q means that Continue is typechecked in an ...
Einstein`s Postulate of Relaavity
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Entanglement in bipartite and tripartite quantum systems

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... black because nothing, not even light, can escape from its event horizon. Even though General Relativity can perfectly well describe black hole dynamics, it cannot explain the physics of the black hole’s interior: the theory blows up in the sense that theoretical calculations based upon General Rela ...
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Effective Field Theories for Topological states of Matter

... There are, however, states with the same symmetry properties, which nevertheless are distinct in a way that I will now describe. Two states are defined to be in the same universality class if one can be obtained from the other by quasi-adiabatically changing the parameters of the Hamiltonian without ...
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Chapter 6 Groups and Representations in Quantum Mechanics

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1. Schrödinger`s Equation for the Hydrogen Atom

... When  = 1, and m = 0 the angle is 90◦ . But when m = ±1 we obtain cos θ = √12 ⇒ θ = 45◦ is the minimum value of θ. The angular momentum vector precesses about the z-axis, maintaining the constant value of θ for a particular value of the quantum number m. You can see that as L becomes larger (i.e., ...
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4 The Schrodinger`s Equation

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Canonical quantization

In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries, of the classical theory, to the greatest extent possible.Historically, this was not quite Werner Heisenberg's route to obtaining quantum mechanics, but Paul Dirac introduced it in his 1926 doctoral thesis, the ""method of classical analogy"" for quantization, and detailed it in his classic text. The word canonical arises from the Hamiltonian approach to classical mechanics, in which a system's dynamics is generated via canonical Poisson brackets, a structure which is only partially preserved in canonical quantization.This method was further used in the context of quantum field theory by Paul Dirac, in his construction of quantum electrodynamics. In the field theory context, it is also called second quantization, in contrast to the semi-classical first quantization for single particles.
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