A coherent state of a harmonic oscillator is a special quantum state encountered in quantum optics. It is an eigenstate of the lowering operator. The eigenvalue relation is âla) = ala) (1) Calculate the expectation value of â in the state Ja). Noting that, The lowering operator â is not Hermitian, so its eigenvalue a is not necessarily a real number. The eigenvalue relation, Eq.(1), in terms of bras is, (alât = a*(a| where a* is the complex conjugate of a.

A coherent state of a harmonic oscillator is a special quantum state encountered in quantum optics. It is an eigenstate of the lowering operator. The eigenvalue relation is âla) = ala) (1) Calculate the expectation value of â in the state Ja). Noting that, The lowering operator â is not Hermitian, so its eigenvalue a is not necessarily a real number. The eigenvalue relation, Eq.(1), in terms of bras is, (alât = a(a| where a is the complex conjugate of a.