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The energy eigenvalues of a system are En = n²E₁. A superposition of n = 4
and n = 5 states is prepared. On measurement the particle can be found in
the n = 4 state with probability P(E4) = 2/7 or in state n = 5 with
probability P(E5) = 5/7.
An experiment is repeatedly performed on a particle prepared in the
superposition state described above. Determine (E) and (E2) in terms of E1,
and hence calculate the uncertainty AE.

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