Alright, I have a kind of dumb question:(adsbygoogle = window.adsbygoogle || []).push({});

Why do I distinguish between dq and dq_{i}when considering the propagation from q_{i}to q to q_{f}?

For example, if we want the wave function at some q_{f}and t_{f}given q_{i}and t_{i}, we may write:

ψ(q_{f},t_{f})=∫K(q_{f}t_{f};q_{i}t_{i})ψ(q_{i},t_{i})dq_{i}

Why do we distinguish between dq_{i}and say, dq, of an intermediate point q?

I understand that a second integration arises, naturally, since another propagator is defined. I just don't get the need to distinguish? I feel like it's almost book-keeping, like we write out (or don't since we use product notation followed by a script D) our dq's so we don't have to write out more integrals...

I know that's not right though, because we treat q and q_{i}as different things...

Some direction would be great...I feel kind of dumb for whatever I'm missing.

edit:

I think I mis-titled this a little, but it's close enough, I hope.

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# Path Integral Basics (Why dimension increases in the integrals?)

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