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A quick question - Quantum Mechanics

  • Thread starter atomqwerty
  • Start date
  • #1
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Just a quick question

A delta Potential is given by -Vδ(x-a). If we wrote the equations of the wave function like this

For E>0

u(x) = Aexp(ikx) + A'exp(-ikx) for x<a
u(x) = Bexp(ikx) + B'exp(-ikx) for x>a

do i have to impose that A'=B=0 in order to u(x) not diverge in when x goes to +-infinite?

The problem is that where I read that, only impose the condition for E<0.

Thanks!!
 

Answers and Replies

  • #2
213
8
but u(x) doesn't diverge at all since exp(+/-ikx) = cos(kx)+/-isin(kx) and this is the unit circle in the C plane. The only boundry condition is that u(a)=u'(a) for x <a , x>a respectivley
 

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