Coefficients in wave function for potential step

[Nick O]

Edit: I forgot to add the picture, and I'm having trouble adding it from Tapatalk. I'll add it soon.

I'm trying to understand the derivation in my textbook of the wave function for a potential step. The derivation reaches the step shown in the attached photo, which I am fine with.

However, the book then says:

One boundary condition is that the wave function ψ2(x) must remain finite, which means that the coefficient B2=0.

Why can't we use this same reasoning to eliminate B1 as well? Clearly the B1 term increases without bound as x approaches negative infinity, exactly as the B2 term does as x approaches positive infinity.

And yet, B1 is later solved in terms of k1, k2, and A1. Any thoughts?

 

[Nick O]

I can't add this to my previous post through Tapatalk. Sorry!

 

[Nick O]

Never mind, my coffee must have been spiked or something. There is no imaginary number in the second wave function.