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## Homework Statement

Usually when we solve the problem of the infinite square well we place one wall at the origin and the other one at, say 2L (please notice the 2).

We get the eigen-energies

[tex]E_n = {{n^2 \pi^2 \hbar^2}\over{8ma^2}}[/tex]

and the eigen-functions

[tex]\psi_n = \sqrt{1\over a}\sin{\left({n\pi\over{2a}}x\right)}[/tex].

My question is this: If instead we placed the well centered about the origin such that the walls are at -L and +L, do we get the same spectrum, and the wave functions shifted left by L, i.e.

[tex]\psi_n = \sqrt{1\over a}\sin{\left({n\pi\over{2a}}(x+L)\right)}[/tex].

?

## Homework Equations

## The Attempt at a Solution

Thing is, when I do it from scratch, I don't get these wavefunctions. I get a combination of sin and cos.