Quantum Mechanics: Outside a (in)Finite Well

[WWCY]

Homework Statement

Referencing image attached.

I'm not sure how the example arrived at ψ ⇒ 0 at x<0 and >L as K ⇒ ∞ in the limiting case of an infinite potential well.

Homework Equations

The Attempt at a Solution

I tried simply applying limits to the wavefuction but in the case x<0, the answer I was arriving at was simply ∞ as the term with constant C approaches 0 and the term with constant D approaches ∞.

I'm also clueless as how ψ ⇒ 0 for x>L.

Can anyone help point out what I'm missing? Thanks in advance.

 

[BvU]

Hi,
From the explanation at (b) you see that D = 0 for x < 0 . Idem C = 0 for x > 0.
Why this is so is indeed not mentioned. So: how can they claim that ?

 

[WWCY]

I see it now, thank you for the insight!

Hi,
Why this is so is indeed not mentioned. So: how can they claim that ?

I assume that this is a possible solution arising out of the Schrödinger equation for a 1D finite well, and that C and D are adjusted to ensure that this wavefunction meets boundary conditions? Is this answer somewhat correct?

 

[BvU]

The wavefunction has to be normalizable. That excludes terms $e^{+x}$ on the far right and $e^{-x}$ on the far left.