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Normalization of wave function (Griffiths QM, 2.5)

  • Thread starter Saraphim
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Homework Statement


A particle in the infinite square well has its initial wave function an even mixture of the first two stationary states:

[itex]\Psi(x,0) = A\left[ \psi_1(x) + \psi_2(x) \right] [/itex]

Normalize [itex]\Psi(x,0)[/itex]. Exploit the orthonormality of [itex]\psi_1[/itex] and [itex]\psi_2[/itex]



Homework Equations


[itex]\psi_n(x) = \sqrt{\frac{2}{a}} \sin \left( \frac{n\pi}{a}x\right)[/itex],
where a is the width of the infinite square well.


The Attempt at a Solution


I've managed to eliminate the orthogonal parts of my integral, so I'm now left with
[itex]|A|^2 \int |\psi_1|^2 + |\psi_2|^2 dx = 1[/itex]

I have the feeling that I now have to exploit the fact that they are both normalized, but why is that so? What's the logic here?

EDIT: I had written a wrong expression for [itex]\psi_n[/itex]. Sorry! :(
 
Last edited:

Answers and Replies

  • #2
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Solution: The expression for [itex]\psi_n[/itex] is already normalized. I should have realized this. Therefore, the integral yields 2 over the interval
 

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