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## Main Question or Discussion Point

It is easily shown that two eigenfunctions with the same eigenvalues can be combined in a linear combination so that the linear combination is itself an eigenfunction. But what if the two eigenvalues are not the same? Can you still find a linear combination of the two functions that is an eigenfunction?

[tex]

aE_1 \psi_1+ b E_2 \psi_2 = E(\psi_1 + \psi_2)

[/tex]

[tex]

aE_1 \psi_1+ b E_2 \psi_2 = E(\psi_1 + \psi_2)

[/tex]