Coefficients in wave function for potential step

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SUMMARY

The discussion focuses on the derivation of the wave function for a potential step, specifically addressing the coefficients B1 and B2. It is established that the coefficient B2 must equal zero to ensure the wave function ψ2(x) remains finite as x approaches positive infinity. The user questions why a similar reasoning does not apply to B1, which also increases without bound as x approaches negative infinity, yet is retained in the solution in terms of k1, k2, and A1. The conversation highlights the importance of boundary conditions in quantum mechanics.

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  • Familiarity with potential step problems in quantum mechanics.
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  • Study the derivation of wave functions in quantum mechanics, focusing on potential step scenarios.
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Students and professionals in physics, particularly those studying quantum mechanics, as well as educators seeking to clarify concepts related to wave functions and potential steps.

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

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

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