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question 6))

The Yukawa potential is given by V°(gamma)(r) = (q)^2/{

4(pi)(eo)0r exp(-°(gamma)r)}, where °(gamma) is a constant. This

describes a screened Coulomb potential.

a)

Sketch the radial dependence of this potential.

b)State the radial SchrÄodinger equation for this potential

c)Assume that °(gamma) is a small parameter. Use ¯rst-order perturbation theory to esti-

mate the energy shift of the ground state of the hydrogen atom when the Coulomb

potential is replaced by the Yukawa potential.

(Hint: The perturbation is w = V(gamma)- Vo