wavefunction is QM
Qmechanic
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# Why is whatdo we hear the square of the wave function?

Assume we superpose two waves of frequencies $$\omega_1, \omega_2$$. Then what we get are beats. Adding the two sines gives us $$\psi = A\sin(\omega_1 t) + A\sin(\omega_2 t) = 2 \sin \left(\frac{\omega_1 + \omega_2}2\right)\cos \left(\frac{\omega_1 - \omega_2}2\right)$$$$\psi = A\sin(\omega_1 t) + A\sin(\omega_2 t) = 2 \sin \left(\frac{\omega_1 + \omega_2}2\right)\cos \left(\frac{\omega_1 - \omega_2}2\right).$$

Then I'd say that the frequency of beats we'd hear is $$\frac{\omega_1 - \omega_2}2$$. On the other hand, someone told me that it's $${\omega_1 - \omega_2}$$ in fact, because what we hear is the square of the wave function $$\psi^2$$.

Why?

marmistrz
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# Why is what we hear the square of the wave function

Assume we superpose two waves of frequencies $$\omega_1, \omega_2$$. Then what we get are beats. Adding the two sines gives us $$\psi = A\sin(\omega_1 t) + A\sin(\omega_2 t) = 2 \sin \left(\frac{\omega_1 + \omega_2}2\right)\cos \left(\frac{\omega_1 - \omega_2}2\right)$$

Then I'd say that the frequency of beats we'd hear is $$\frac{\omega_1 - \omega_2}2$$. On the other hand, someone told me that it's $${\omega_1 - \omega_2}$$ in fact, because what we hear is the square of the wave function $$\psi^2$$.

Why?