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Is there a theorem that says that for linear operators a and b on some vector space, if
[tex] [b , b^\dagger] = [a, a^\dagger] = 1 [/tex],
where [A, B] denotes the commutator AB-BA, then there exists a unitary operator U such that
[tex] b = UaU^\dagger [/tex]
[tex] [b , b^\dagger] = [a, a^\dagger] = 1 [/tex],
where [A, B] denotes the commutator AB-BA, then there exists a unitary operator U such that
[tex] b = UaU^\dagger [/tex]