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A particle in 1D potential well

  1. Dec 11, 2013 #1
    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.
     
  2. jcsd
  3. Dec 11, 2013 #2

    ChrisVer

    User Avatar
    Gold Member

    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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