The Scattering Operator in Quantum Mechanics I the Properties of the Scatterin
The Scattering Operator in Quantum Mechanics I the Properties of the Scatterin
Harry E Moses
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We shall now define H Q and V and indicate the quantum variables. As H we take the sum of the kinetic energy operator of the incident particle and o the Hamiltonian of the scatterer. The perturbation is taken to be inter- action between the incident particle and the scatterer. Let us denote by the subscript 1 the operators associated with the incident particle and by the subscript 2 the operators associated with the scatterer. Then x^ denotes the set of coordinates of the incident particle and ...x 2 the coordinates associated with the scatterer. If the scatterer is a heavy atom, x„ will denote collectively the coordinates which give the position of each of the electrons. We shall assume that in the x representation the perturbation V is a function of x, and x^ V* - V(^, x 2 ) which decays rapidly when |x.. J is large. Then the operator H is the sum of the operators H o - T l * H 2 - 77 - where T is the kinetic energy operator of the incident particle and HL is the Hamiltonian of the scatterer.
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