# Finding an energy of a particle in an infinite potential well

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,
• I was not referring to the energy-time uncertainty principle. I was just confused about the definiteness in the measurement of Energy. Another similar confusion I had was with the uncertainty in the measurement of x. If I were to locate the particle's position inside the potential well, it means $\Delta$x is $0$. But what does it mean to truly know where the particle exactly is? And if that does make sense, what does it mean for uncertainty in momentum to be infinite? I am very sure I am missing something quite fundamental here. – Ufomammut Dec 7 '18 at 23:20