- #1

happyparticle

- 400

- 20

- Homework Statement
- Show that a vector is an eigenvector of an operator

- Relevant Equations
- ##A|a\rangle = a|a\rangle##

Hi,

If ##|a\rangle## is an eigenvector of the operator ##A##, I know that for any scalar ##c \neq 0## , ##c|a\rangle## is also an eigenvector of ##A##

Now, is the ket ##F(B)|a\rangle## an eigenvector of ##A##? Where ##B## is an operator and ##F(B)## a function of ##B##.

Is there way to show that ##F(B)|a\rangle## is and eigenvector of ##A## and find the eigenvalue?

Thank you!

If ##|a\rangle## is an eigenvector of the operator ##A##, I know that for any scalar ##c \neq 0## , ##c|a\rangle## is also an eigenvector of ##A##

Now, is the ket ##F(B)|a\rangle## an eigenvector of ##A##? Where ##B## is an operator and ##F(B)## a function of ##B##.

Is there way to show that ##F(B)|a\rangle## is and eigenvector of ##A## and find the eigenvalue?

Thank you!