- #1
Shafikae
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Consider a hydrogen atom whose wave function is at t=0 is the following superposition of energy eigenfunctions [tex]\psi[/tex]nlm(r)
[tex]\Psi[/tex](r, t=0) = [tex]\frac{1}{\sqrt{14}}[/tex] *[2[tex]\psi[/tex]100(r) -3[tex]\psi[/tex]200(r) +[tex]\psi[/tex]322(r)
What is the probability of finding the system in the ground state (100? in the state (200)? in the state (322)? In another energy eigenstate?
For this part i found each eigen state and put it into an integral. Should there be limits of integration for r? If so, from where to where? I did the integration for (100) and (200) but for (322) i got something crazy.
What is the expectation value of the energy: of the operator L2, of the operator Lz
I have no clue what to do here.
[tex]\Psi[/tex](r, t=0) = [tex]\frac{1}{\sqrt{14}}[/tex] *[2[tex]\psi[/tex]100(r) -3[tex]\psi[/tex]200(r) +[tex]\psi[/tex]322(r)
What is the probability of finding the system in the ground state (100? in the state (200)? in the state (322)? In another energy eigenstate?
For this part i found each eigen state and put it into an integral. Should there be limits of integration for r? If so, from where to where? I did the integration for (100) and (200) but for (322) i got something crazy.
What is the expectation value of the energy: of the operator L2, of the operator Lz
I have no clue what to do here.