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Unformatted text preview: E = mc 2 for a particle at rest. (i) Find the masses (i.e. energies) m 1 and m 2 of the states which are eigenvectors of H . Let the diagonal elements of H be h ν μ  H  ν μ i = m μ , h ν e  H  ν e i = m e . 1 You may assume that  A  <<  m em μ  . (ii) The eigenstates ν 1 and ν 2 of H can be written as linear combinations of the states  ν μ i and  ν e i  ν 1 i = cos θ  ν e i sin θ  ν μ i ,  ν 2 i = sin θ  ν e i + cos θ  ν μ i . Find the mixing angle θ in terms of A,m e ,m μ with again  A  <<  m em μ  . (iii) Suppose at time t = 0, a ν μ is produced at rest in the laboratory. What is the probability as a function of time that this state will actually be observed as a ν e ? Express the answer in terms of m 1 ,m 2 and θ . 2...
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 Spring '10
 Sghy
 mechanics, Particle Physics, Electron, Angular Momentum, Momentum, Muon

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