# Mode of vibration comparing Classical and Quantum waves

I'm now studying Quantum Mechanics, and I took a course on Vibration and Waves last year. I have been trying to make an analogy between classical and the quantum waves. Is it true that both the modes of a quantum and classical wave can not be excited individually?

Whenever you pluck a classical string, its motion can be described as a superposition of many different modes , n=1,2,3... you can never excite a single mode.

In analogy, can we say that whenever you try to measure the wave function, the measured value will be a composition of different eigenvalues?

Any ideas or contributions much appreciated.

No, that is a bad analogy. In fact, you've got things precisely the wrong way around. Whenever you perform a measurement that's in a state that is a superposition of basis states (eigenstates of the Hamiltonian, for instance) $$\psi=\sum\limits_n c_n \psi_n$$ where the $c_n$ are complex constants (arbitrary up to normalization) then this measurement will always return a value that is exactly the eigenvalue of one of these basis states. For instance, if we have $$\psi=\frac{1}{\sqrt{6}}(\psi_1+\psi_2+2\psi_3)$$ then a measurement will always return the eigenvalue corresponding to either $\psi_1, \psi_2$ (each with probability $\frac{1}{6}$) or $\psi_3$ (probability $\frac{2}{3}$).