hw7 - t g τ in each of the four n = 2 states n l m = 2 1...

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HOMEWORK # 7 Physics 6572 Friday, 10/31/08; due 11/7/08 1. Estimate the ground state energy of a helium atom by the variational principle. Use the hydrogen-like wave functions as the trial functions and confirm the results given in class. 2. A hydrogen atom in its ground state ( { n, l, m } = { 1 , 0 , 0 } ) is placed between the plates of a capacitor. A time-dependent but spatially uniform electric field (not potential!) is applied as follows: E = braceleftbigg 0 for t < 0 E 0 e - t/τ for t > 0, (1) where E 0 is in the positive z -direction. Using first-order time-dependent perturbation theory, compute the probability for the atom to be found at
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Unformatted text preview: t g τ in each of the four n = 2 states: { n, l, m } = { 2 , 1 , ± 1 } , { 2 , 1 , } , { 2 , , } . 3. The ground state of a hydrogen atom is subjected to a time-dependent potential as follows: V ( x , t ) = V cos( kz-ωt ). (2) Using time-dependent perturbation theory, obtain an expression for the transition rate at which the electron is emitted with momentum p . Show, in particular, the angular distribution of the ejected electron in terms of θ and φ deFned with respect to the z-axis....
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