Quantum Mechanics Solution Manual 

© Leon van Dommelen 

2.3.6 Solution dotf
Question:
Verify that the most general multiple of that is normalized on the interval 0 is where is any arbitrary real number. So, using the Euler formula, the following multiples of are all normalized: , (for 0), , (for ), and , (for 2).
Answer:
A multiple of means , where is some complex constant, so the magnitude is
You can always write as where is some real angle, and then you get for the norm:
So for the multiple to be normalized, the magnitude of must be 1/, but the angle can be arbitrary.