If a very small uniform-density sphere of charge is in an clectrostatic potential V(r), its potential energy is U(r) = V(r) +rởV²V(r) + ·…, where r is the position of the center of the charge and ro is its very small radius. The "Lamb shift" can be thought of as the sinall correction to the energy levels of the hydrogen atom because the physical electron does have this property. If the r term of U is treated as a very small perturtbation compared to the Coulomb interaction V (r) : shifts for the 1s and 2p levels of the hydrogen atom? Express your result in terms of ro and fundamental constants. The uuperturbed wave functious are = -c? /r., what are the Lanb -3/2.e-r/anY; bzpm(r) V24 1 b16(r) = 2a,/2. -5/2 re-r/2aBYm -7/20BY, %3D where as = h2 /mee?.
If a very small uniform-density sphere of charge is in an clectrostatic potential V(r), its potential energy is U(r) = V(r) +rởV²V(r) + ·…, where r is the position of the center of the charge and ro is its very small radius. The "Lamb shift" can be thought of as the sinall correction to the energy levels of the hydrogen atom because the physical electron does have this property. If the r term of U is treated as a very small perturtbation compared to the Coulomb interaction V (r) : shifts for the 1s and 2p levels of the hydrogen atom? Express your result in terms of ro and fundamental constants. The uuperturbed wave functious are = -c? /r., what are the Lanb -3/2.e-r/anY; bzpm(r) V24 1 b16(r) = 2a,/2. -5/2 re-r/2aBYm -7/20BY, %3D where as = h2 /mee?.
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Transcribed Image Text:If a very small uniform-density sphere of charge is in an clectrostatic
potential V(r), its potential cnergy is U(r) = V(r) + rởV²V(r) + -…,
where r is the position of the center of the charge and ro is its very small
radius. The “Lamb shift" can be thought of as the sinall correction to the
energy levels of the hydrogen atom because the physical electron does have
this property. If the r term of U is treated as a very small perturbation
compared to the Coulomb interaction V (r) = -c2/r., what are the Lanb
shifts for the 1s and 2p levels of the hydrogen atom? Express your result
in terms of ro and fundameutal constants.
The umperturbed wave functions are
P16(r) = 2a,2.
-3/2. e-r/anY; bzpm(r) :
1
-5/2
re-r/20BYm
%3D
V24
where as =
h? /mee?.
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