and the quantization procedure is complete.
We see that the dynamical algebra of the operators \(\hat{\boldsymbol{n}}\)\(a\), and \(a^{\dagger}\)is the same as of the simple harmonic oscillator, so it is the Hilbert space spanned by the \(\left|n\right\rangle\) states. What is distinct among the several possible choices of the parameters \(\left(g,\omega, \mathcal{F}\right)\) are the behavior of the physical characteristic functions of the model, as the energy values, expected values, and others.

Eigenvalue solutions, eigenfunctions, and uncertainty

Let us now show the explicit form of the number operator: