A system of N harmonic oscillators of frequency w are prepared in identical initial states of wavefunction Þ(x,0). It is found that the measurement of the energy of the system at t = 0 gives 0.5hw with probability 0.25, 1.5hw with probability 0.5 and 2.5hw with probability 0.25. a. Write a possible function (x, 0). b. Write the corresponding p(x, t). c. What is the expectation value of the Hamiltonian in the state p(x,t) ?
A system of N harmonic oscillators of frequency w are prepared in identical initial states of wavefunction Þ(x,0). It is found that the measurement of the energy of the system at t = 0 gives 0.5hw with probability 0.25, 1.5hw with probability 0.5 and 2.5hw with probability 0.25. a. Write a possible function (x, 0). b. Write the corresponding p(x, t). c. What is the expectation value of the Hamiltonian in the state p(x,t) ?
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Transcribed Image Text:3. A system of N harmonic oscillators of frequency w are prepared in identical initial states of
wavefunction Þ(x,0). It is found that the measurement of the energy of the system at t = 0
gives 0.5hw with probability 0.25, 1.5hw with probability 0.5 and 2.5hw with probability
0.25.
a. Write a possible function p(x, 0).
b. Write the corresponding (x, t).
c. What is the expectation value of the Hamiltonian in the state p(x,t) ?
d. Calculate the expectation value of position at time t
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