Observable quantities ("observables") are represented by Hermitian operators. One definition of a Hermitian operator is that its expectation value is real. In order for a possibly complex number to be real, it must be equal to its complex conjugate. For example, the operator Â, which represents the observable A, satisfies (Â) = (Â)* Using the definition of expectation value, [v* (Av) dx = [v(Âv)* dz The right-hand-side can be rearranged v (Av) dx = [(A)* Vdx I* Prove this last relation for the momentum operator, p = -iho/ax. Hint: Apply integration- by-parts on the left side of the equation, and use the fact that the wave function is normalizable.

Observable quantities ("observables") are represented by Hermitian operators. One definition of a Hermitian operator is that its expectation value is real. In order for a possibly complex number to be real, it must be equal to its complex conjugate. For example, the operator Â, which represents the observable A, satisfies (Â) = (Â)* Using the definition of expectation value, [v* (Av) dx = [v(Âv)* dz The right-hand-side can be rearranged v (Av) dx = [(A)* Vdx I* Prove this last relation for the momentum operator, p = -iho/ax. Hint: Apply integration- by-parts on the left side of the equation, and use the fact that the wave function is normalizable.