Consider the amplitude for a free particle to propogate from [itex]\vec{x}_0[/itex] to [tex]\vec{x}[/tex]:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

U(t) = \left\langle \vec{x} | e^{-i H t} | \vec{x}_0 \right\rangle

[/tex]

I guess I don't understand what it means for a particle to propogate from one "position" to the next. If the particle is not in a position eigenstate, then it does not have a well-defined position. If so, then how can we even talk about propogating from one position to the next.

Bottom line: [itex] | \vec{x}_0 \rangle [/itex] is a wave and does not have a well-defined position. So how can we talk about positions?

I am seeking clarification on this.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Propogation Amplitude

**Physics Forums | Science Articles, Homework Help, Discussion**