Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
1. Ehrenfest Theorem. (a) Prove that for a quantum particle of mass m and described by a wave function 4(x, t), -∞ av(x) Hint: where the expectation value on the right-hand side is given by (-aV(x)/ax) = - foox 14(x, t)|² dx (b) Use the equation above to determine the equation of motion for . (c) Compare your result in (b) to the (x) for the harmonic oscillator potential V(x) = mw²x² classical equation of motion of the harmonic oscillator * + w²x = 0 and comment on the comparison d (p) dt d²(x) dt² m = m- d²(x) dt² = = (-ƏV(x)/Əx), 个

1. Ehrenfest Theorem. (a) Prove that for a quantum particle of mass m and described by a wave function 4(x, t), -∞ av(x) Hint: where the expectation value on the right-hand side is given by (-aV(x)/ax) = - foox 14(x, t)|² dx (b) Use the equation above to determine the equation of motion for . (c) Compare your result in (b) to the (x) for the harmonic oscillator potential V(x) = mw²x² classical equation of motion of the harmonic oscillator * + w²x = 0 and comment on the comparison d (p) dt d²(x) dt² m = m- d²(x) dt² = = (-ƏV(x)/Əx), 个

icon
Related questions
Question

HANDWRITTEN THEN BOX THE FINAL ANSWERS

Solve the following problems. Write your solutions clearly and in detail in a short bond paper or yellow paper. 1. Ehrenfest Theorem. (a) Prove that for a quantum particle of mass m and described by a wave function Y(x, t), Hint: d (p) dt where the expectation value 2|4(x, t)|² dx av (x) -100 ax on the right-hand side is given by (-aV(x)/ax) = (b) Use the equation above to determine the equation of motion for . (c) Compare your result in (b) to the (x) for the harmonic oscillator potential V(x) = mw²x² classical equation of motion of the harmonic oscillator * +w²x = 0 and comment on the comparison = m d²(x) dt² d²(x) dt² m. -= (-ƏV(x)/ax), ↑
Transcribed Image Text:Solve the following problems. Write your solutions clearly and in detail in a short bond paper or yellow paper. 1. Ehrenfest Theorem. (a) Prove that for a quantum particle of mass m and described by a wave function Y(x, t), Hint: d (p) dt where the expectation value 2|4(x, t)|² dx av (x) -100 ax on the right-hand side is given by (-aV(x)/ax) = (b) Use the equation above to determine the equation of motion for . (c) Compare your result in (b) to the (x) for the harmonic oscillator potential V(x) = mw²x² classical equation of motion of the harmonic oscillator * +w²x = 0 and comment on the comparison = m d²(x) dt² d²(x) dt² m. -= (-ƏV(x)/ax), ↑
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer