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 Exercise [22.03] 
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Joined: 03 Jun 2010, 15:18
Posts: 136
Post Exercise [22.03]
Attached my solution


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30 Sep 2010, 17:27

Joined: 12 Jul 2010, 07:44
Posts: 154
Post Re: Exercise [22.03]
Your solution seems overcomplicated to me.
You don't need to go back to considering integrals over R!
All you need to do is note that:

\left\langle\chi\middle|\chi\right\rangle = \left\langle a \phi + b \psi \middle| a \phi + b \psi \right\rangle<br />= |a|^2 \left\langle\phi\middle|\phi\right\rangle + |b|^2 \left\langle\psi\middle|\psi\right\rangle + \overline{a}b \left\langle\phi\middle|\psi\right\rangle + a\overline{b} \left\langle\psi\middle|\phi\right\rangle

Since \phi and \psi are given to be normalizable, this result is finite (and hence \chi is normalizable) iff \left\langle\psi\middle|\phi\right\rangle and \left\langle\phi\middle|\psi\right\rangle are finite. But exercise [22.02] has already established that they are.


07 Oct 2012, 06:16
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