The wave function is given by (x, t) = C3e-iwitp,(x) + 4e-i@2tp2(x)] where p1(x) and p2(x) are energy eigenfunctions that are orthonormal, and w, = 3.0 x 1015 Hz and w, = 7.5 × 1015 Hz. %3D What are the two energy levels in units of eV? Calculate the average energy of the system in eV.
The wave function is given by (x, t) = C3e-iwitp,(x) + 4e-i@2tp2(x)] where p1(x) and p2(x) are energy eigenfunctions that are orthonormal, and w, = 3.0 x 1015 Hz and w, = 7.5 × 1015 Hz. %3D What are the two energy levels in units of eV? Calculate the average energy of the system in eV.
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Transcribed Image Text:**Question:**
Calculate the standard deviation expected when measuring the energy many times at \( t = 20 \, \mu s \) after the system is prepared in an identical manner. Keep the units in eV.
![The wave function is given by
\[
\psi(x, t) = C \left[ 3e^{-i\omega_1 t} \phi_1(x) + 4e^{-i\omega_2 t} \phi_2(x) \right]
\]
where \(\phi_1(x)\) and \(\phi_2(x)\) are energy eigenfunctions that are orthonormal, and \(\omega_1 = 3.0 \times 10^{15}\, \text{Hz}\) and \(\omega_2 = 7.5 \times 10^{15}\, \text{Hz}\).
**Questions:**
1. What are the two energy levels in units of eV?
2. Calculate the average energy of the system in eV.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e50119e-8646-4255-90fd-98958ba58941%2Fcdd662eb-b4c5-4f79-a321-90d558c8d167%2Fevcb8fe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The wave function is given by
\[
\psi(x, t) = C \left[ 3e^{-i\omega_1 t} \phi_1(x) + 4e^{-i\omega_2 t} \phi_2(x) \right]
\]
where \(\phi_1(x)\) and \(\phi_2(x)\) are energy eigenfunctions that are orthonormal, and \(\omega_1 = 3.0 \times 10^{15}\, \text{Hz}\) and \(\omega_2 = 7.5 \times 10^{15}\, \text{Hz}\).
**Questions:**
1. What are the two energy levels in units of eV?
2. Calculate the average energy of the system in eV.
Expert Solution
Step 1
Given:
The given wavefunction is
The angular frequency values are
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