The order of the quantities in the numerator must be preserved because α is an operator. For exam-
ple, if an operator is d / dx , it is easy to see that (2 x )( d / dx )(2 x ) (2 x )(2) 4 x is not the same as
( d / dx )(2 x )(2 x ) ( d / dx )(4 x
2 ) 8 x .
If the wave function φ is normalized, the denominator in Eq. (2.18) is equal to 1. Therefore, the value
of a is given by the relationship