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**Analytical solutions of S.E. for "unusual" potential**

Hi,

Given the potential

V(x)=0, when x<0 (region I)

V(x)=V_0, when 0<=x<=a, V_0=real constant (region II)

V(x)=infinite when x>a (region III)

What would be the general form on the solutions for each region?

I would think the solution for region I would be on the form A*exp(ikx) rather than A*exp(ikx)+B*exp(-ikx), since the exp(-ikx) term would "blow up" when x -> -infinite ?? But in the problem text I'm asked later "name the coefficient for the right-moving term A, and the left-moving term B", implying that I should use two terms for the solution ... ?