Adjoint Operator Homework: Clarifying Complex Conjugates

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Homework Statement



Hello,

I need some things clarified before I can do my homework. They have to do with the adjoint operator. Say I have an operator P and its adjoint is P(dagger). I noticed that the complex conjugate of the adjoint gives back the operator. Does that mean the adjoint is just the complex conjugate?
 
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No, that's not true. If you represent the operator as a matrix, you'll find the adjoint is the conjugate of the transposed matrix. It's not simply the conjugate.
 

Thread 'Number of quantum accessible states of a particle given T, N?'

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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