Problem 4.15 A hydrogen atom starts out in the following linear combination of the stationary states n = 2, 1 = 1, m 1 and n 2, 1 1, m = -1: V(r. 0) = 1 (W211+V21-1). (a) Construct V(r, t). Simplify it as much as you can. (b) Find the expectation value of the potential energy, (V). (Does it depend on t?) Give both the formula and the actual number, in electron volts.
Problem 4.15 A hydrogen atom starts out in the following linear combination of the stationary states n = 2, 1 = 1, m 1 and n 2, 1 1, m = -1: V(r. 0) = 1 (W211+V21-1). (a) Construct V(r, t). Simplify it as much as you can. (b) Find the expectation value of the potential energy, (V). (Does it depend on t?) Give both the formula and the actual number, in electron volts.
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Transcribed Image Text:Exercise 4
Problem 4.15 A hydrogen atom starts out in the following linear combination of
the stationary states n = 2, 1 = 1, m 1 and n 2, 1 1, m = -1:
1
V(r. 0) =
(211+ V21-1).
(a) Construct (r, t). Simplify it as much as you can.
(b) Find the expectation value of the potential energy, (V). (Does it depend on
r?) Give both the formula and the actual number, in electron volts.
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Why don't you include the time dependent part of the wave equation when finding the expectation value of the potential? I don't see how the modulus of the wave function gets rid of the time dependent part. Can you please explain?
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