What Are Eigenstates and Their Role in Quantum Mechanics?

[knightpraetor]

I've read the chapter but it hasn't helped. Eigenstates are states with a definite amount of energy independent on time? and then any other state is a linear combination of the eigenstates, with some Cn acting as a weighting factor...is there a limitation on what the Cn's can be? otherwise, wouldn't non-stationary states be unquantized?

 

[Hargoth]

In fact, the $|c_n|^2$ are the probabilities of measuring the energy value $E_n$. Remember that quantum mechanics assumes that the wave function collapses to an energy-eigenstate when the energy is measured, so the measured energy is still quantized.

This "collapse" means the wavefunction is

$\Psi = \sum \limits _n c_n \varphi_n$ before the energy is measured, where the $|c_n|^2$ say how probable it is to measure energy $E_n$.

Right after the measurement of energy $E_n$, the wavefunction collapses to

$\Psi = \varphi_n$.