Exercise 6.14 Consider a hydrogen atom whose state at time t = 0 is given by 1 (7,0) = A$200 (7) +√311 (7) +√739422(7), where A is a normalization constant. (a) Find A so that the state is normalized. (b) Find the state of this atom at any later time t. (c) If a measurement of the energy were carried out, what values would be found and with what probabilities?
Exercise 6.14 Consider a hydrogen atom whose state at time t = 0 is given by 1 (7,0) = A$200 (7) +√311 (7) +√739422(7), where A is a normalization constant. (a) Find A so that the state is normalized. (b) Find the state of this atom at any later time t. (c) If a measurement of the energy were carried out, what values would be found and with what probabilities?
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Please help with EXERCISE 6.14 and 6.15
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Exercise 6.14
Consider a hydrogen atom whose state at time t = 0 is given by
1
1
(7,0) = A$200 (7) +11 (7) + 3422(7),
where A is a normalization constant.
(a) Find A so that the state is normalized.
(b) Find the state of this atom at any later time t.
(c) If a measurement of the energy were carried out, what values would be found and with
what probabilities?
(d) Find the mean energy of the atom.
6.6. EXERCISES
389
Exercise 6.15
Calculate the width of the probability density distribution for r for the hydrogen atom in its
ground state: Ar = (²) 10- (r)10.
0.10
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