49.46 An atom makes a transition from an excited state with a lifetime of 10^-9

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49.46 An atom makes a transition from an excited state with a lifetime of 10^-9 s to the ground state and emits a photon with a wavelength 600 nm. What is the uncertainty in the energy of the excited state? What is the percentage uncertainty if the energy is measured from the ground state? (a) Show that the function psi = x e^ -ax^2 is an eigenfunction of the operator d^2/dx^2 - 4a^2x^2. What is the eigenvalue? (b) Show that the function psi = K e^r/k is an eigenfunction of the operator d/dr. What is the eigenvalue?

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