Hey /sci/
I want to measure a position. The operator for position is
$\hat{x}\psi=x\psi$
After applying the measurement, the vector state changes from $\psi$ to $x\psi$, which collapses the wave function. Nevertheless, the new state should still evolve according to Schrödinger's equation. The problem is, when I try to test it, I find the new state no longer satisfies the Schrödinger equation. When I try to do it, I get:
$ix\hbar\partial_{t}\psi=-\frac{\hbar^2}{2m}(x\partial_{xx}+2\partial_{x})\psi
What am I doing wrong?
I want to measure a position. The operator for position is
$\hat{x}\psi=x\psi$
After applying the measurement, the vector state changes from $\psi$ to $x\psi$, which collapses the wave function. Nevertheless, the new state should still evolve according to Schrödinger's equation. The problem is, when I try to test it, I find the new state no longer satisfies the Schrödinger equation. When I try to do it, I get:
$ix\hbar\partial_{t}\psi=-\frac{\hbar^2}{2m}(x\partial_{xx}+2\partial_{x})\psi
What am I doing wrong?
