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at the very end of this lecture

http://www.ph.ed.ac.uk/~pmonthou/Statistical-Mechanics/documents/SM10.pdf [Broken]

and the very beginning of this lecture

http://www.ph.ed.ac.uk/~pmonthou/Statistical-Mechanics/documents/SM11.pdf [Broken]

we look at evaluating this sum by making it into an integral by two different methods :

(i) the sum and integral are both in n-space

(ii) the sum in n-space is converted into either an integral in k-space or energy space.

How do you know which method to use? would it just depend on the information given to you in an exam, i.e. if you were given say [itex]g(\epsilon)[/itex] you would realise you have to convert to energy space - or am i completely missing the point here?

http://www.ph.ed.ac.uk/~pmonthou/Statistical-Mechanics/documents/SM10.pdf [Broken]

and the very beginning of this lecture

http://www.ph.ed.ac.uk/~pmonthou/Statistical-Mechanics/documents/SM11.pdf [Broken]

we look at evaluating this sum by making it into an integral by two different methods :

(i) the sum and integral are both in n-space

(ii) the sum in n-space is converted into either an integral in k-space or energy space.

How do you know which method to use? would it just depend on the information given to you in an exam, i.e. if you were given say [itex]g(\epsilon)[/itex] you would realise you have to convert to energy space - or am i completely missing the point here?

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