After watching this video: and some ones on noethers theorem (geometric as opposed to algebraic understanding) I think my analogy was quite close, I think my question is ultimately interpretational.
Umm, what?
My understanding of momentum is essentially “how much something is effected when an object hits”, i.e. quantity of motion. Yet I'm actually confused as to whether there is a separate wave function in position representation, to a wave function in momentum representation. Like, what...
I'm a QM noob/newb trying to understand the physical implication of a wave packet, in my mind it is something like this:
On the x-axis there is displacement (vibration), probability on the y. I Imagine stretching and compressing the wave packet. When I stretch it out, the amplitude must...