Projection Operator help in quantum mechanics! thanks~?

Question

how do you show that |j>?

Thank you~

Answer 1

A projection operator is defined by the property (idempotence):

PP = P

To prove that for:

P = |j>
you need to assume that |j> is normalized so that = 1. In that case:

PP = |j> = |j> = P

Also, if |v> is any vector:

P |v> = |j> = u |j>

where u= (some scalar). This is an eigenvector of P with eigenvalue 1 if and only if:

u |j> = |v>

in other words if and only if |v> is any scalar multiple of |j>. (In general, eigenvectors are unique only to within multiplication by a scalar). The operator |j>. That is, it preserves any scalar multiple of |j> and kills any vector orthogonal to |j>

Answer 2

Actually it has two eigenvalues: 1 and 0.

Answer 3

hi Nuff; i for my section experience, with unquestionably no scientific information, that each selection we make on a daily basis provides an danger for an option ( or parallel universe). I join the Robert A. Heinlein concept, in all probability beforehand a while yet, an astounding fiction author. attempt "The style of The Beast" or "Stranger In a wierd Land"reliable gentle relaxing reads. yet time is a severe subject, and one i'm afraid I even have very fastened notions upon. As i think God created it,and holds it till, as you would be able to assert the time is optimal, and guy ought to flow forward purely, living each and each 2d to the fullest, as there is not any going back. "The previous is history, the destiny a secret, we can purely stay interior the now." yet to punch a hollow into an option universe, will in all probability happen sooner or later, what occurs next? nicely which would be an entire distinctive universe lower back. LOL have relaxing with this one! Bob