# Quantum states after real world measurements

Regarding measurements of an observable in a quantum system. My understanding, from the postulates of quantum mechanics, is that when we measure an observable quantity, the state of the system collapses to an eigenfunction of the linear Hermitian operator which corresponds to the observable: $$\hat{A}|\psi \rangle = y|y \rangle$$ where $y$ is the eigenvalue and $|y \rangle$ is the eigenstate. Then if we project onto the basis of the observable we get the dirac delta function. Let's consider the position operator for example, then:

$$\langle x| \hat{A}|\psi \rangle = y \langle x| y \rangle = y \delta(x-y).$$

From what I understand, in real world measurements the state of the system is not exactly a dirac delta function but rather some wave packet. What is the nature of this wave packet and what determines the shape and corresponding function thereof? Why can't the function be a dirac delta function in real world measurements?

Thanks.

• Related to, and possibly a duplicate of physics.stackexchange.com/questions/218947/… – DanielSank Jul 29 '16 at 17:46
• @DanielSank His question is way too advanced. I'm looking for a much more basic discussion, I'm just starting to learn QM. – user100411 Jul 29 '16 at 17:51
• I really think these questions are almost identical. Please note that my question is not more advanced than yours, it's more more specific (particularly in terms of notation) because I know a bit more about the subject so was able to ask a more focused question. I guess you're more asking why we don't get delta functions, while I was asking for an explanation of the final wave function, whatever it may be. – DanielSank Jul 29 '16 at 17:57
• I think the already-existing answer by Ian is good. However, I would encourage someone who knows about such things to provide an explanation or at least a reference on how to actually calculate the evolution of a quantum state as it is being imperfectly measured. – DanielSank Jul 29 '16 at 18:02
• The collapse postulate is quite controversial. Read Cini quantum measurement without collapse – Boltzee Jul 29 '16 at 19:03