- #1
safekhan
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Q: Using Dirac notation, show that if A is an observable associated with the operator A then the eigenvalues of A^2 are real and positive.
Ans: I know how to prove hermitian operators eigenvalues are real:
A ket(n) = an ket(n)
bra(n) A ket(n) = an bra(n) ket(n) = an
[bra(n) A ket(n)]* = an* bra(n) ket(n) = an*
[bra(n) A(dager) ket(n)] =[bra(n) A ket(n)] = an*
therefore, an*=an
But, I don't know how to treat an operator^2 and start this question.
Ans: I know how to prove hermitian operators eigenvalues are real:
A ket(n) = an ket(n)
bra(n) A ket(n) = an bra(n) ket(n) = an
[bra(n) A ket(n)]* = an* bra(n) ket(n) = an*
[bra(n) A(dager) ket(n)] =[bra(n) A ket(n)] = an*
therefore, an*=an
But, I don't know how to treat an operator^2 and start this question.