Answered: 6. Consider an electron in a hydrogen… | bartleby

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6. Consider an electron in a hydrogen atom in a state given by
Y(t=0):
√5 {0311(¹,0,9) +20 ³310 (¹, 0,9)}
a. If you measured the energy what values can you get, and what is the probability of
each?
b. Find the expectation value of the L²
c. Find (L) as a function of time.

Expert Solution

Step 1

Given that,

the state of an electron in the hydrogen atom is

$Ψ (t = 0) = \frac{1}{\sqrt{5}} \{Φ_{311} (r, θ, φ) + 2 Φ_{310} (r, θ, φ)\}$

To find

a) The energy of the state and the probability of each state.

b) The expectation value of $L^{2}$

c) The value of $<L_{x}>$ function of time

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