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An Operator is defined as P|x> = |-x>,
1. Is P^2 a Projector operator?
2. What are the eigen value and eigen function of P?
1. Is P^2 a Projector operator?
2. What are the eigen value and eigen function of P?
Thank you Compuchip!Be careful, P is not a projector operator (P² is not equal to P); the question asks if P² is a projection operator.
alpha, What is the definition of such an operator?
what you have there is a parity operator and they have eigenvalues [tex]\pm1[/tex] and the most generic eigenfunctions I can think of are [tex] A(e^{kx} \pm e^{-kx}) ; k \in C [/tex] respectively for the +1 and -1 eigenvaluesThank you Compuchip!
I am asking about P. Yes, I know that P^2|x> = |x> which is not equal to p|x>. So it is not projection operator. My next confusion is can I write
|-x> = -|x> ?
How can we calculate the eigen value and eigen function of P