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Sorry if this question is not very challenging, but Im driving myself to confusion...

I happily derived the eigen functions for an infinite square well spanning from 0 to L and found them to be:

...in agreement with wikipedia.

However my course notes derive solutions for an inf sq well between -a and +a.

Surely L=2a, no?

In the notes n=1,3,5... produces cosine solutions and n=2,4,6... produce sine solutions.

Why is there now cosine solutions?

Please help, I'm going crazy :)