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Infinite Well: Parity

The wave functions have the symmetry property
$\displaystyle \phi_n(x+L/2)=(-1)^{n-1}\phi_n(L/2-x),$     (254)

that is they are symmetric or antisymmetric with respect to the symmetry point $ x=L/2$ of the infinite well potential $ V(x)$, in alternating order with the quantum number $ n$. The lowest eigenstate $ \phi_1(x)$ is symmetric and has no node, the next eigenstate $ \phi_2(x)$ is anti-symmetric and has one node, $ \phi_3(x)$ is again symmetric and has two zeros, and so on.

We recognize that conceptually, everything is really completely analogous (the counting from 0 or $ 1$ is a matter of convention).



Tobias Brandes 2004-02-04