The discussion centers on the action of the operator \((N+1)^{-1/2} \alpha\) on the ket state \(|n\rangle\) of a harmonic oscillator. The number operator \(N\) satisfies the eigenvalue equation \( \hat{N}|n\rangle = n|n\rangle\). The operator can be interpreted using a Taylor series expansion, specifically \((1 + N)^{-1/2} = 1 - \frac{1}{2}N + \frac{3}{8}N^2 + \dots\). This formulation is linked to the Susskind operator, which is crucial for understanding non-polynomial functions of operators in quantum mechanics.
PREREQUISITESQuantum physicists, students of quantum mechanics, and researchers interested in operator theory and harmonic oscillator dynamics.
To make sense of a non-polynomial function of an operator, you can interpret it as a Taylor series:Jean-Mathys du bois said:Summary:: how does the operator (N+1)^-1/2 α act on a |n> state of harmonic osciliator? N is the number operator N|n>=n|n> and α anihilation operator
I tried playing with the number's operator eigenvalues equation but couldn't get anywhere, can s/b help me out?