Stationary-state scattering

• If ?(x,x',t) = |?(x,t)> < ?(x',t)|

  • and ?(x,t) = u(x) exp(ihE/t)
  • then ?(x,x',t) = |u(x)> < u(x')|
  • - independent of time. h

• Evolution eqn. for time-independent ?(x,x'):

  • (H0 – iW)x?x,x' – ?x,x'(H0 – iW)x' + 2i?Wx?x,x'?Wx' = 0
  • Two-coordinate x,x' second-order p.d.e.
  • Energy E only appears in the boundary conditions.

• hh

• hdhhhh

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