[a, true for photons, assume th pilation operators satisfy ââ

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Instead of a commutation relation [â, ât] = 1
which is true for photons, assume that the creation
and annihilation operators satisfy âât + â†â = 1
Show that the number operator N = âtâ satisfies
âN = (1 – N)â
%3D
â'Ñ = (1 – Ñ)ât
3
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.)
Transcribed Image Text:Instead of a commutation relation [â, ât] = 1 which is true for photons, assume that the creation and annihilation operators satisfy âât + â†â = 1 Show that the number operator N = âtâ satisfies âN = (1 – N)â %3D â'Ñ = (1 – Ñ)ât 3 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.)
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