What Does ψ_0(x) = <x|0> Represent in Dirac Notation?

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Do not solve the problem just look at the picture.

http://i208.photobucket.com/albums/bb33/DanusMax/giro2_zps11d2056b.jpgWell its the end of the semester and I found out that I had only one of the required books for my undergraduate course.

Anyways back to the question. As you can see in the photo what I would like to know is what
ψ_0(x)= <x|0>. stands for?

I haven't seen examples of how to use it or anything. I do know that it can be broken up and something can be placed in the center <x|?|0>.

what i don't know is what that x is or why there's a zero on the other side. What does it mean I would like to have examples if possible.
 
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The \mid 0 \rangleindicates the ground state. The \langle x\mid is the bra for "x" basis state, which is the state associated with the position x.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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