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I am new to QM, have find some wavefunction in different potentials, but there we need to normalize the wave function, for a reason that - particle should be found somewhere . So a wave-function, to be related to a particle need to be normalizable. But in scattering, there is no notion of normalization!

Aren't the solutions in scattering states related to some particle?

Qmechanic
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Taxicab
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1 Answers1

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Mathman - when we study scattering we assume that we have a flux of multiple particles headed at some target and the question we want to answer is "which way do they go when they bounce off?". The end result of the endeavor is to find the relative intensity of the deflected flux in any given direction.

Since we imagine the end result for any given scattered particle will look like a plane wave it can't be normalized in the sense of, say, an atomic orbital. To put this another way, atomic orbitals are bound states and can be normalized. Incoming flux and outgoing scattering are plane waves - and the analogy to normalization would be conservation of flux.

Paul Young
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  • So if there are more than one particle, then also there need to be a analogy in while mathematically treating it.. – Taxicab Feb 05 '19 at 14:55
  • Yes, the flux of the incoming scattered beam must be equal to the integral of all the outgoing flux over all directions. However, in practice, this is not of interest because it is the pattern of the scattering which is studied. In most real world experiments the incoming flux is messy and much does not even "hit" the target so the conservation of flux rule is "usually" only theoretically interesting. But, yes - the analogy to normalization of a bound state in scattering is conservation of flux for the unbound states - both incoming and outgoing. – Paul Young Feb 05 '19 at 15:14