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2. Free Fields
2. Free Fields

... The typical information we want to know about a quantum theory is the spectrum of the Hamiltonian H. In quantum field theories, this is usually very hard. One reason for this is that we have an infinite number of degrees of freedom — at least one for every point ~x in space. However, for certain the ...
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... o Ex:  Chemical Change: a change in the composition of materials creating a _________________________________ with totally new properties. (you can NOT get the old substance back) o Ex: Indicators of a Chemical Change:  Gas Liberations: _________________ is formed and you observe bubbles  Heat an ...
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... Pair production is the creation of an elementary particle and its antiparticle, for example an electron and its antiparticle, the positron, a muon and antimuon, or a tau and antitau. Usually it occurs when a photon interacts with a nucleus, but it can be any other neutral boson, interacting with a n ...
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... Today we accept Bohr’s idea about light being emitted by an atom or ion owing to its (electron) transitions between allowable energy states. According to his theory, the allowable energies of the hydrogen atom are the allowable energies the electron can have in the atom. A given energy value that co ...
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wave concepts
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... other forms of electromagnetic radiation surround us every moment of our lives and although we do not directly “see” their waves, aside from visible light, these phenomena can all be understood in terms of waves. Furthermore, we show later that matter also behaves as a wave and that our current quan ...
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... • A rotation around the x direction can be achieved by driving the red-sidebands for both orbitals. • A rotation around z can be achieved by Stark shifting one of the orbitals. ...
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... OR THE FIRST FEW decades of this century there did not seem to be any trouble in saying what is meant by an elementary particle. J. J. Thomson could use the electric field in a cathode-ray tube to pull electrons out of atoms, so atoms were not elementary. Nothing could be pulled or knocked out of el ...
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Exam #: Printed Name: Signature: PHYSICS

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Sep 17 - BYU Physics and Astronomy

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... profound meaning to this? 4. Origin of the Natural Laws. The two combinations contain all electron-positron properties. Charge depends on whether there is a + or amplitude of the IN wave at the center. If a resonance is superimposed upon an anti-resonance, they annihilate. The amplitude at the cente ...
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... Thus, the electromagnetic field is not self-adjoint and there must exist anti-photons [9]. Why do we not see those? The explanation follows from considering the conserved quantities, mass and energy. In a matter island of the universe, two states of a certain energy difference always have a mass dif ...
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... nebulae would undergo a shift to the red by Compton effect on those free electrons. Now the admissible deflection in one single process is very small, the angular size of the nebulae being indeed less than one degree of arc. For the change in wave-length AX by a single Compton scattering within the ...
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... General Periodic Trends – descending a group atomic radii increase, and with s & p blocks they decrease from left to right across period. Period 6 is different, due to lanthanide contraction. The 4f orbitals are being occupied by the lanthanides, and these have poor shielding properties. The repulsi ...
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... that still retain their quantum wave natures? To answer these questions we need rules for building larger objects out of smaller ones, and means of applying them. These rules are the subject of this unit, and they lead to some surprising macroscopic quantum behavior such as Bose-Einstein condensates ...
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... or quasihole, it follows that there is a finite energy gap for such a change, and the fractional quantum Hall state is therefore said to be “incompressible”. This is true within the naive model we have used so far: when we come to study the behavior at the edges of the sample we will see that in a s ...
Solutions - Illinois State Chemistry
Solutions - Illinois State Chemistry

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Wave–particle duality

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