Consider one quantum particle in a 3D box in the microcanonical ensemble. It's energy eigenvalues are:
\begin{equation*} \varepsilon = \frac{h^2}{8mL^2} (n_x^2+n_y^2+n_z^2) \end{equation*} The question is, when computing the microstates in this system, why do we only count energy eigenstates? In other words, why not counting possible superpositions too.
With only these two states i can make infinitely many different states:
\begin{equation*} \alpha |1,0,0\rangle + \beta |0,1,0\rangle \end{equation*}
A related concept is, when calculating the partition function, why do we only sum over energy eigenstates. Or, more generally, why do we only need to sum over a complete basis.
This is an old doubt i've had since i first studied statistical mechanics.
Related questions i've found but haven't really made it clearer for me.
