In one dimension the normalized momentum eigenstate for a particle with periodic boundary conditions of length L is: [tex]\psi_k(x)=\frac{1}{\sqrt{L}}e^{ikx} [/tex].(adsbygoogle = window.adsbygoogle || []).push({});

Is the completeness relation obvious:

[tex]\Sigma \psi_k(x)\psi_{k}(0)=\frac{1}{L}\Sigma e^{ikx}e^{-ik0}=\frac{1}{L}\Sigma e^{ikx}=\delta(x) [/tex]

where the sum is over discrete eigenstates k?

How would you go about proving that sum?

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# Box normalization

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