solk(1) - Physics 742 Graduate Quantum Mechanics 2 Solution...

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Physics 742 – Graduate Quantum Mechanics 2 Solution Set K 1. [15] An electron of mass m scatters from a neutral hydrogen atom in the ground state located at the origin. (a) [7] What is the charge distribution for a neutral hydrogen atom? Don’t forget the nucleus! What is the Fourier transform of the charge? As a check, you might want to make sure it vanishes when K = 0, since the atom is neutral. The nucleus has charge e and is locate at the origin, so we can model it with a charge distribution () () 3 e ρδ = rr . The electron is spread out in a wave function given by 2 e ρψ =− . Using the explicit form of the wave function for the ground state, we therefore have 0 2 3 3 0 ra e ee a π we will have to keep or e ’s straight. When computing the Fourier transform, the charge distribution is spherically symmetric, so there’s no harm in The Fourier transform of this is () 0 1 2 33 2 00 0 10 1 1 2 0 3 cos 1 00 1 0 0 22 2 0 cos exp cos 4 cos 2 2c o s o s 8 21 1 2 4 ii r de e d e e edr d r i K r aaa ed e a i K ai K a K iK a iKa iKa K
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This note was uploaded on 02/15/2011 for the course PHYS 742 taught by Professor Unknow during the Spring '04 term at Harvard.

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solk(1) - Physics 742 Graduate Quantum Mechanics 2 Solution...

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