Question

Let the operator A_op correspond to an observable of a particle. It is assumed to have just two eigenfunctions ?1(x) and ?2(x) with distinct eigenvalues. The function corresponding to an arbitrary state of the particle can be written as

?(x) = c1?1(x) + c2?2(x).

An operator B_op is defined according to

B_op*?(x) = c2?1(x) + c1?2(x).

Prove that B_op is Hermitian.

5.8. Let the operator Aop correspond to an observabl a particle. It is assumed to have just two eigenfunctio vj (x) and pr2(x) with distinct eigenvalues. The fu corresponding to an arbitrary state of the particle ca written as An operator Bop is defined according to Prove that Bop is Hermitian.

Answer 1

"Since A_op is an observable, is Hermitian operat or, psi_1(x) and (psi_2(x) are orthogonal => lang psi_1