2. A three-state system has energy eigenfunctions $1(x), Þ2(x) and $3(x) with correspondingenergy eigenvalues -ħw, 0, ħw respectively.The system is in the initial state of wavefunctionp(x, 0) = c1 $1(x) + c2$2(x) + 2c2¢2(x)where w, C1, C2 are positive real constants.If the expectation value of the Hamiltonian in this state is equal to -0.64hwa. Obtain c1 and c2b. Write the normalized wavefunction (x, t)c. Determine the uncertainty in energy AE in the state of wavefunction (x, t)d. What is the probability of measuring the energy ħw at time t?

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Science

Physics

F2$2(x)

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter39: Introduction To Quantum Physics

Section: Chapter Questions

Problem 30P

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Question

2. A three-state system has energy eigenfunctions $1(x), Þ2(x) and $3(x) with corresponding
energy eigenvalues -ħw, 0, ħw respectively.
The system is in the initial state of wavefunction
p(x, 0) = c1 $1(x) + c2$2(x) + 2c2¢2(x)
where w, C1, C2 are positive real constants.
If the expectation value of the Hamiltonian in this state is equal to -0.64hw
a. Obtain c1 and c2
b. Write the normalized wavefunction (x, t)
c. Determine the uncertainty in energy AE in the state of wavefunction (x, t)
d. What is the probability of measuring the energy ħw at time t?

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