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Consider the delta function potential well :V(x) = −αδ(x) (α > 0). (a) What are the boundary...

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Physics

Consider the delta function potential well :V(x) = −αδ(x) (α> 0).

(a) What are the boundary conditions on the bound state wavefunction and its derivative at x = ±∞ and x = 0? Explain. Hint: Youmay find the property stated in Prob. 2 useful.

(b) Show that there is only one bound state.

(c) Find the energy E and wave function ψ(x) of the boundstate.

(d) Find the transmission coefficient for scattering states,with energy E > 0 and incident form the left

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