If a very small uniform-density sphere of charge is in an electrostatic potential V(r), its potential energy is U(r) - V

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If A Very Small Uniform Density Sphere Of Charge Is In An Electrostatic Potential V R Its Potential Energy Is U R V 1 (33.69 KiB) Viewed 82 times

If a very small uniform-density sphere of charge is in an electrostatic potential V(r), its potential energy is U(r) - V(r) + VV(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 small correction to the energy levels of the hydrogen atom because the physical electron does have this property. If the rở term of U is treated as a very small perturbation compared to the Coulomb interaction V(r) = -e/r, what are the Lamb shifts for the 1s and 2p levels of the hydrogen atom? Express your result in terms of ro and fundamental constants. The unperturbed wave functions are exp(-r/aY. 2pr(r) = 3 8/?r exp(-r/203)Y"//24, where as = /mee? 1:() = 2073/2