I'm reading through the Introduction to Quantum Mechanics book by Griffiths (2nd edition)(adsbygoogle = window.adsbygoogle || []).push({});

and it is describing delta-function potential wells.

When it describes how to find bound states the energy is E < 0 (negative) in the region x < 0 (negative).

It says the general solution is:

[tex]\psi (x) = Ae^{-\kappa x} + Be^{\kappa x}[/tex]

It explains that as x goes to -∞ the first term blows up. Which makes sense because it will go to infinity, while the second term only goes to zero.

However, they then look at the situation when E > 0, x < 0

again the general solution is:

[tex]\psi (x) = Ae^{-\kappa x} + Be^{\kappa x}[/tex]

but this time they say that neither term blows up. I don't understand why that is. Shouldn't the first term still go to infinity as x goes to -∞ ?

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# Delta-function potentials, scattering states

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