ch39-p043 - 43. The proposed wave function is 1 er a 32 a =...

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43. The proposed wave function is ψ = 1 32 π a e ra where a is the Bohr radius. Substituting this into the right side of Schrödinger’s equation, our goal is to show that the result is zero. The derivative is d dr a e =− 1 52 π so r d dr r a e 2 2 π and 11 2 1 1 2 1 2 2 r d dr r d dr a e ar a F H G I K J + L N M O Q P + L N M O Q P π . The energy of the ground state is given by Em e h 4 0 22 8 ε and the Bohr radius is given by ah m e E e a == 2 0 8 ππ ε 0 ,. so The potential energy is given by Ue r 2 4 πε 0 , so 88 84 8 8 12 1 12 2 2
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