Construct a theory for \(N\) bosons in an isotropic two-dimensional trap. This corresponds to a trap in which the energy level spacing due to excitations in the \(z\) direction is much larger than the spacing in the other directions. Determine the density of states \(a(\varepsilon)\) of this system. Can a Bose-Einstein condensate form in this trap? If so, find the critical temperature as a function of the trapping frequencies and \(N\). How much larger must the frequency in the third direction be for the system to display two-dimensional behavior?