I attached the solution but i want t know the steps how to find that solution The solution

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I attached the solution but i want t know the steps how to find
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(c) (/10) As k + 0, both d=o and di=1 found in (b) tend to zero, but Si=1 dies out much faster, so we will take di=1 (and in general any diz1 to be 1 negligibly small relative to 81=0). In this limit, calculate the total cross- section o for this potential for s-wave scattering. Show that your solution converges to the result from hard-sphere scattering found in lecture in the appropriate limit.
E = ²K2/(2m), where K² = ka + kõ, and ko = V2mVo/h2. h =
where 70 K cot(Ka) - a In the limit ka + 0, we get that yoka? tan(80) = (2 ) 1+ya
(c) The total cross section is given by 47 0 = k2 I=0 (21+1) sin?(81) If we are only interested in s-wave scattering, we need to only consider do which according to Equation (2) would yield 2 2 -- () - - σ 41 yoka k2 = 4πα? 1 tan(Ka) Ka (4) 1+ya You did not need to do this, but you can do a simple sanity check: In the limit of hard sphere scattering (Vo → oo or equivalently K → 00, so that tan(Ka) +0) so that we arrive at o = - 47a², the same result as hard sphere scattering Ka