I'm covering a book on QM, and just started recently and I'm stuck at understanding something. It says that we can describe the state of motion of a particle with an infinite plane wave equation:
It says that it corresponds to a motion with precisely defined momentum.
"but having amplitudes $|\psi|=const. \forall r,t $, the infinite harmonic plane waves leave the position of the particle entirely unspecified."
- What does the word "infinite" aim to imply here? Does it mean we assume the imaginary "waves" extend infinitely in both directions? Also, if so, does that matter?
- Of course any planar wave has constant amplitude! It's not that they are imposing some mathematical restriction on the wave. Please explain the statement.