Question

6. An electron in hydrogen atom is in initial state ?(r,0) = A(2?_{100} + i?_{210} + ?_{21,-1} - 2i?_{211}) where ?_{nlm} are the eigenfunctions of the hydrogen atom. a. Determine the constant A b. What is the probability of finding the electron in the first excited state? c. Write the state ?(r,t) at time t, using energy eigenvalues as E_n = -?^2 / n^2 d. Find the expectation value of L in the state ?(r,t). e. Find the expectation values of L_x and L_y in the state ?(r,t). f. If measurement of L_z led to the value -?, what will be the results of the measurement of energy and the square of the total orbital momentum immediately afterwards and what are their probabilities?

          6. An electron in hydrogen atom is in initial state
?(r,0) = A(2?_{100} + i?_{210} + ?_{21,-1} - 2i?_{211})
where ?_{nlm} are the eigenfunctions of the hydrogen atom.
a. Determine the constant A
b. What is the probability of finding the electron in the first excited state?
c. Write the state ?(r,t) at time t, using energy eigenvalues as E_n = -?^2 / n^2
d. Find the expectation value of L in the state ?(r,t).
e. Find the expectation values of L_x and L_y in the state ?(r,t).
f. If measurement of L_z led to the value -?, what will be the results of the measurement of energy and the square of the total orbital momentum immediately afterwards and what are their probabilities?

6. An electron in hydrogen atom is in initial state
?(r,0) = A(2?100 + i?210 + ?21,-1 - 2i?211)
where ?nlm are the eigenfunctions of the hydrogen atom.
a. Determine the constant A
b. What is the probability of finding the electron in the first excited state?
c. Write the state ?(r,t) at time t, using energy eigenvalues as En = -?^2 / n^2
d. Find the expectation value of L in the state ?(r,t).
e. Find the expectation values of Lx and Ly in the state ?(r,t).
f. If measurement of Lz led to the value -?, what will be the results of the measurement of energy and the square of the total orbital momentum immediately afterwards and what are their probabilities?

Added by Denise S.

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