Recent content by crises

What if the Hamiltonian is such that for a given time difference the particle can not be at position $x_2$ starting from position $x_1$ ? For example, a particle with $p=1$ and $m=1$ has a Hamiltonian $H=\frac{1}{2}$. Suppose 1-D. Then if $x_1=0$ and $x_2=1$ $ \Delta T=1$. So the integral is a...

I am currently starting with my first qft lectures and i am trying to see for the free particle that the propagator $$ <x_i | e^{-i\frac{p}{2m} T|x_f}>$$ will equal to one if x_f = 1, x_i=0 m=1 u=1 p=1, T=1 and $$\hbar \rightarrow 0$$ or 0 otherwise. I understand that this limit will result in...