Instead of a commutation relation [â, â¹] = 1which is true for photons, assume that the creationand annihilation operators satisfy ââ† + â¹â = 1Show that the number operator N = â¹â satisfiesâÑ = (1 - Ñ)âatŃ = (1-N)atProve that if one eigenvalue of N is n = 0, there isonly one other eigenvalue, n = 1. (This means thatthere cannot be more than one particle in theparticular state associated with the operators¡ât and â.)

Given: Let us consider the given, a^,a^T=1a^a^++a^+a^=1 Let's determine, a) The number operator…

Instead of a commutation relation [â, â¹] = 1 which is true for photons, assume that the creation and annihilation operators satisfy âât +â¹â = 1 Show that the number operator N = â¹â satisfies âÑ = (1 – Ñ)â â¹Ñ = (1 - №)ât Prove that if one eigenvalue of N is n = 0, there is only one other eigenvalue, n = 1. (This means that there cannot be more than one particle in the particular state associated with the operators ¡ât and â.)

Instead of a commutation relation [â, â¹] = 1 which is true for photons, assume that the creation and annihilation operators satisfy âât +â¹â = 1 Show that the number operator N = â¹â satisfies âÑ = (1 – Ñ)â â¹Ñ = (1 - №)ât Prove that if one eigenvalue of N is n = 0, there is only one other eigenvalue, n = 1. (This means that there cannot be more than one particle in the particular state associated with the operators ¡ât and â.)