# S-Matrix Peskin and Schroeder

On the Page no.102, Last Paragraph of Peskin and Schroeder,

...If we set up $$|\phi_\mathcal{A}\phi_\mathcal{B}\rangle$$ in the remote past, and then take the limit in which the wavepackets $$\phi_i(\mathbf{k}_i)$$ become concentrated about the definite momenta $$\mathbf{p}_i$$, this defines an in state..

What is the limit in which wave packets become concentrated about definite momenta? What did the book mean by this?

In the distant past, the interaction part of the Hamiltonian is zero, and hence the Hamiltonian is a free (non-interacting) Hamiltonian. This means that at $$t=-\infty$$, the eigenstates of the Hamiltonian have definite momenta. We take these to be our `in' states.