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

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