Consider N identical and indistinguishable quantum harmonic oscillators of frequency ω. They are not interacting each ot
Posted: Wed Jul 06, 2022 11:41 am
Consider N identical and indistinguishable quantum harmonicoscillators of frequency ω. They are not interacting each other.The Hamiltonian of a single oscillator is given by H = Ћω (a†a + ½)where a† and a are creation and annihilation operators,respectively. (a) Show that the partition function of a singleoscillator is given by Z1 = e-βЋω/2 /(1- e-βЋω/2 ) (b) Find themean energy per oscillator. (c) Show that when kT >> Ћω, theclassical equipartition rule holds. That is U/N→kT.