2. A three-state system has energy eigenfunctions Þ1(x), Þ2(x) and $3(x) with corresponding energy eigenvalues -hw, 0, hw respectively. The system is in the initial state of wavefunction Þ(x, 0) = c1$1(x)+ cz¢z(x)+ 2cz$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 c, 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 hw at time t?
2. A three-state system has energy eigenfunctions Þ1(x), Þ2(x) and $3(x) with corresponding energy eigenvalues -hw, 0, hw respectively. The system is in the initial state of wavefunction Þ(x, 0) = c1$1(x)+ cz¢z(x)+ 2cz$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 c, 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 hw at time t?
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Transcribed Image Text:2. A three-state system has energy eigenfunctions $1(x), Þ2(x) and $3(x) with corresponding
energy eigenvalues -hw, 0, hw respectively.
The system is in the initial state of wavefunction
Þ(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 hw at time t?
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