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1. Is P^2 a Projector operator?

2. What are the eigen value and eigen function of P?

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- #1

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1. Is P^2 a Projector operator?

2. What are the eigen value and eigen function of P?

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Try acting again with the operator P

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alpha, What is the definition of such an operator?

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CompuChip said:

alpha, What is the definition of such an operator?

Thank 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

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alphaneutrino said:Thank 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

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 eigenvalues

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