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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 | H | i = m , h e | H | e i = m e . 1 You may assume that | A | << | m e-m | . (ii) The eigenstates 1 and 2 of H can be written as linear combinations of the states | i and | e i | 1 i = cos | e i -sin | i , | 2 i = sin | e i + cos | i . Find the mixing angle in terms of A,m e ,m with again | A | << | m e-m | . (iii) Suppose at time t = 0, a 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 e ? Express the answer in terms of m 1 ,m 2 and . 2...
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