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-iwit, The wave function is given by (x, t) = c[3e-i@it&1(x) + 4e-iw2t¢2(x)] where 1(x) and 2(x) are energy eigenfunctions that are orthonormal, and w, = 3.0 x 1015 Hz and w2 = 7.5 x 1015 Hz.

-iwit, The wave function is given by (x, t) = c[3e-i@it&1(x) + 4e-iw2t¢2(x)] where 1(x) and 2(x) are energy eigenfunctions that are orthonormal, and w, = 3.0 x 1015 Hz and w2 = 7.5 x 1015 Hz.

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**Transcription:** 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. --- For educational purposes, this text is asking for the analysis of variability in energy measurements for a system over repeated trials. The focus is on calculating the standard deviation, which is a statistical measure of the dispersion of a set of values. Here, the energy is to be measured at 20 microseconds after the system's preparation, and the results should be expressed in electron volts (eV).
Transcribed Image Text:**Transcription:** 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. --- For educational purposes, this text is asking for the analysis of variability in energy measurements for a system over repeated trials. The focus is on calculating the standard deviation, which is a statistical measure of the dispersion of a set of values. Here, the energy is to be measured at 20 microseconds after the system's preparation, and the results should be expressed in electron volts (eV).
The wave function is given by \[ \psi(x, t) = C[3e^{-i\omega_1 t} \phi_1(x) + 4e^{-i\omega_2 t} \phi_2(x)] \] 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 \( \omega_2 = 7.5 \times 10^{15} \text{ Hz} \).
Transcribed Image Text:The wave function is given by \[ \psi(x, t) = C[3e^{-i\omega_1 t} \phi_1(x) + 4e^{-i\omega_2 t} \phi_2(x)] \] 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 \( \omega_2 = 7.5 \times 10^{15} \text{ Hz} \).
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