Quantum Mechanics Solution Manual |
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© Leon van Dommelen |
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2.3.6 Solution dot-f
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.