When applying quantum mechanics, we often concentrate on states that qualify as "ortho...

When applying quantum mechanics, we often concentrate on states that qualify as "orthonormal." The main point is this: If we evaluate a probability integral over all space of ψ1*ψ1 or of ψ2*ψ2 we Set (unsurprisingly), but if we evaluate such an integral for ψ1*ψ2 or ψ2*ψ1 we get 0. This happens to be true for all the systems where we have tabulated or actually derived sets of wave functions (e.g., the particle in a box,

the harmonic oscillator, and the hydrogen atom), By integrating over all space, show that expression (7-44) is not normalized unless a factor of  is included with the probability.