How to Solve the Creation Operator Problem in Problem 3a?

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Anyone having an idea of how to solve problem 3a) file:///C:/Users/Administrator/Downloads/handin1%20(2).pdf ?

I've been stuck for a great while but have not idea.
 
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on part 3b) is it correct to argue that since you integrate away the x-dependence in the number operator that according to the Heisenberg equation [H,N]=0 since both the partial derivative and total derivative of N is zero?
 
You know, I'm having a great deal of difficulty reading that file. :w Maybe you could hold it up a little closer to *my* screen?
 
Why can't you read the file? file:///C:/Users/administrator/Downloads/handin1%20(2).pdf
 
befj0001 said:
Why can't you read the file? file:///C:/Users/administrator/Downloads/handin1%20(2).pdf
Because it's on your computer!
 
It's given a gas of particles all identical which has T fixed and spin S. Let's ##g(\epsilon)## the density of orbital states and ##g(\epsilon) = g_0## for ##\forall \epsilon \in [\epsilon_0, \epsilon_1]##, zero otherwise. How to compute the number of accessible quantum states of one particle? This is my attempt, and I suspect that is not good. Let S=0 and then bosons in a system. Simply, if we have the density of orbitals we have to integrate ##g(\epsilon)## and we have...
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