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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.