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Quantum Mechanics with Basic Field Theory by Bipin R. Desai

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20 Scattering in three dimensions – a formal theory

In this chapter we go to three dimensions and formalize the scattering theory without going through time-dependent perturbation theory. We solve our problems through the function that plays a pivotal role in physics, the Green’s function. We define the S-matrix, the T-matrix, and their connection to the scattering amplitude.

20.1 Formal solutions in terms of Green’s function

 

We will present here a formal way, invoking the Green’s function technique, to obtain the scattering solutions in terms of abstract state vectors and operators. This will also allow us to define two very important quantities in scattering theory, the T- and S-matrices.

We start with the energy eigenvalue equation for ...

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