Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S18 / 2 / 1 / Solution

For $E<0$, impose decay and continuity on $G=C{e}^{-\kappa |x-x^{\prime }|}$. Its derivative jump is $-2\kappa C$, so $-{\hslash }^2(G_{+}^{\prime }-G_{-}^{\prime })/(2m)=1$ requiresThere is no nonzero free solution decaying at both infinities that can be added without spoiling the derivative condition.