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I'm currently working my way through Dirac's Quantum Mechanics, and I found this proof really irritating.

We're trying to demonstrate that any eigenket can be expressed as a sum of eigenkets of a real linear function [itex]\xi[/itex] which satisfies the equation [itex]\varphi[/itex]([itex]\xi[/itex]) = a[itex]_{1}[/itex][itex]\xi[/itex][itex]^{n}[/itex]+a[itex]_{2}[/itex][itex]\xi[/itex][itex]^{n-1}[/itex]...+a[itex]_{n}[/itex]

I attach Dirac's proof. I'm confused by how 22 vanishing for [itex]\chi (\xi)[/itex] in general follows from the substitution.

Thanks.

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# Eigenvector proof from Dirac's QM

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