# What the wave function looks of a particle in the infinite square well looks like after collapse for measurements of position and energy

Consider a particle in a the infinite square well from x=0 to x=L. At t=to, I make a measurement of position and get x=L/2. What is the resulting wave function at t=to? My understanding, from reading, is that it is the dirac delta function with the spike at L/2. This makes sense to me, but I just want to confirm my logic. And then I can treat this function as the initial state and use schrodinger's equation to see how it evolves with time, right?

Additionally, if I make a a measurement of energy some time after - what is the function going to look like? This idea is more blurry to me. Will the collapsed function be expressed in a different vector space?

So for a position measurement, it is the delta function in space; for energy measurements, it is one of the eigenstates of the Hamiltonian (in this case, sinusoidal functions of position that go to zero at the walls of the well, $x=0$ and $x=L$).