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?
Thanks in advance.