This question arises from a discussion I recently had with my friend. We were talking about a particle in an infinite potential well. The particle is in an arbitrary wavefunction $\Psi$. When one measures the energy of the particle, then he gets a specific value $E_1$, which is an eigen value corresponding to an eigen-state of the particle $\psi_1$, to which the system has been forced to be in by making the measurement. The part that tricked us is: How can anyone know with definite certainty what the value of energy is for a quantum particle? Shouldn't there exist some uncertainty in the value of $E$?
Do you refer to the energy-time principle involving the product $\Delta E \Delta t?$ Here, $\Delta E$ is the resulting standard deviation you obtain on measuring $E$ in an infinite number of identically prepared quantum systems. In the case of the system in an eigenstate of energy $E$ (through e.g a collapse as per the Copenhagen interpretation), you will always measure $E$ and so here the standard deviation $\Delta E = 0$.
Now, to satisfy the principle constraint it means $\Delta t$ is infinite. As emphasised within this thread,
this is a reflection that there is no finite time in which one will measure a deviation in the energy of the state.