# Path Integral Formulation: Allowable Paths?

1. Jun 14, 2012

### referframe

In Feynman’s Path Integral formulation of QM, one starts by considering all possible paths between two fixed space-time events.

Question: Must the wave-length associated with each allowable path divide evenly into the spatial length of the path?

2. Jun 14, 2012

### Sonderval

Perhaps I'm stupid right now, but as far as I can see there is no such thing as a wavelength in the path integral - you just integrate over the action. If you have a free particle and consider a path taken with constant velocity, the phase given by exp(iS) will rotate with constant rate - in this case you could define something like a "wavelength" as the distance between two points of equal phase, but there is no need for this phase to have the same value at the end as at the starting point.

3. Jun 16, 2012

### stevendaryl

Staff Emeritus
No, Feynman's path integral considers all possible paths, where a path is just a function from time to position. He doesn't even restrict it to continuous functions, let alone functions with a definite wavelength.