A particle in 1D potential well

  • Thread starter White_M
  • Start date
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Hello,

What does it means when a particle having mass "m" in a one dimentional potential well has the potential given by:
V(x)=
[itex]\stackrel{-\alpha δ(x) for |x|<a}{∞ for |x|≥a}[/itex]

where δ(x) is the delta function and [itex]\alpha[/itex] is a constant.

I understand that the well boundries have infinite potential but what about the well? Does it have -[itex]\alpha[/itex] potential only for x=0? What is the potential for |X|<a and x≠0? And how do I write the boundry conditions here?

10x!
Y.
 

ChrisVer

Gold Member
3,328
437
the potential in for X>a or X<-a is infinite
the potential on point X=0 is -infinite due to the delta function (but its integral for example is not).
the rest |X|<a and not 0, the potential is zero.

The boundary conditions on +/-a are the same (your wavefunction must vanish).
http://en.wikipedia.org/wiki/Delta_potential
 

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