In class we worked out the following(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\int e^{ik(x-X)}dk=\frac{e^{ik(x-X)}}{i(x-X)}\approx \frac{sin[k(x-X)]}{x-X}

[/tex]

by taking the real part of the solution. My teacher wants us to graph the following functions

[tex]

\psi_{1} \sim \frac{sin(x)}{x}

[/tex]

[tex]

\psi_{2} \sim \frac{sin(x)}{x}-\frac{1}{2}\frac{sin(2x)}{2x}

[/tex]

The second function, though, has a little dip in it at 0 that shouldn't be there. He says that's due to the fact that the functions aren't normalized and that we should be doing Gram-Scmidt or some other procedure to obtain the proper results. However, when I do Gram-Schmidt I get something nasty that can't possibly be correct (and most importantly, doesn't correct the problem). So what am I doing wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Orthonormalizing functions

**Physics Forums | Science Articles, Homework Help, Discussion**