Problem 2.13 A particle in the harmonic oscillator potential starts out in the state Y (x. 0) = A[3¥o(x) + 4¼1(x)]. (a) Find A. (b) Construct ¥ (x, t) and |¥(x. t)F. (c) Find (x) and (p). Don't get too excited if they oscillate at the classical frequency; what would it have been had I specified 2(x), instead of y1(x)? Check that Ehrenfest's theorem (Equation 1.38) holds for this wave function. (d) If you measured the energy of this particle, what values might you get, and with what probabilities?
Problem 2.13 A particle in the harmonic oscillator potential starts out in the state Y (x. 0) = A[3¥o(x) + 4¼1(x)]. (a) Find A. (b) Construct ¥ (x, t) and |¥(x. t)F. (c) Find (x) and (p). Don't get too excited if they oscillate at the classical frequency; what would it have been had I specified 2(x), instead of y1(x)? Check that Ehrenfest's theorem (Equation 1.38) holds for this wave function. (d) If you measured the energy of this particle, what values might you get, and with what probabilities?
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![Problem 2.13 A particle in the harmonic oscillator potential starts out in the state
¥ (x. 0) = A[3¥o(x)+ 4¼1(x)].
(a) Find A.
(b) Construct ¥ (x, t) and |¥(x. t)P.
(c) Find (x) and (p). Don't get too excited if they oscillate at the classical
frequency; what would it have been had I specified ¥2(x), instead of Vi(x)?
Check that Ehrenfest's theorem (Equation 1.38) holds for this wave function.
(d) If you measured the energy of this particle, what values might you get, and
with what probabilities?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d2fdd51-a813-4b36-89e9-f9581acfc2ee%2Fbacc6d69-5a8d-4525-bff5-db4fddd7cb94%2Fi8hmo1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 2.13 A particle in the harmonic oscillator potential starts out in the state
¥ (x. 0) = A[3¥o(x)+ 4¼1(x)].
(a) Find A.
(b) Construct ¥ (x, t) and |¥(x. t)P.
(c) Find (x) and (p). Don't get too excited if they oscillate at the classical
frequency; what would it have been had I specified ¥2(x), instead of Vi(x)?
Check that Ehrenfest's theorem (Equation 1.38) holds for this wave function.
(d) If you measured the energy of this particle, what values might you get, and
with what probabilities?
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