Advanced Quantum Mechanics II PHYS 40202

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To be used in future

Prev Section 5.9: Brownian Motion Up Chapter 5: Path Integrals Section 5.11: Partition sum Next

5.10 Time-ordered Perturbation Theory

Let

We assume we know the propagtor

for

. We get

We expand in powers of

, and get

Taylor expanding, we find that

We now use the trick that we can order the

time integration variables in

different ways to put them in increasing order of time

and find that

We now split

into the same time intervals, and find that

This is the basic equation of time-ordered perturbation theory.

There is a very neat alternative way to write this expression

Prev Section 5.9: Brownian Motion Up Chapter 5: Path Integrals Section 5.11: Partition sum Next