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**Unformatted text preview: **α > 0. Remember that, ( ) x δ = 0, , x x ≠ ∞ = ; and ( ) 1 x dx ∞-∞ = ∫ ; and ( ) ( ) ( ) f x x a dx f a ∞-∞-= ∫ (a). By integrating the SEQ from – ε to + ε , then taking the limit as ε → 0, show that the condition on the derivative of the wavefunction, d ψ /d x , for the case of the delta function potential is given by: ( ) 2 2 d d m dx dx ε α +--= -ℏ (b). Qualitatively sketch the wavefunction for this potential (it should look familiar!). (c). What are the solutions (x) to the SEQ in regions I and II (see figure above)? (d). By applying the continuity condition on at x=0, as well as the condition derived in (a) above, derive bound state energy E associated with the wavefunction you sketched in (b). x V(x) -αδ (x) V=0 E I II +0 -0...

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