Consider the Hamiltonian for a (large) number (N) of oscillators (hat{a}_{i}, hat{a}_{i}^{dagger}) (with (left[hat{a}_{i}, hat{a}_{j}^{dagger} ight]=delta_{i j})

Consider the Hamiltonian for a (large) number \(N\) of oscillators \(\hat{a}_{i}, \hat{a}_{i}^{\dagger}\) (with \(\left[\hat{a}_{i}, \hat{a}_{j}^{\dagger}\right]=\delta_{i j}\) ):

where \(\hat{a}_{N+1} \equiv \hat{a}_{1}, \hat{a}_{N+1}^{\dagger} \equiv \hat{a}_{1}\). Diagonalize it and find its eigenstates.

Transcribed Image Text:

H = = N i=1 a+ (a; +h.c.)], (8.107)