Do you know some example of an operator, other than momentum or position, that has (at least partially) continuous spectrum with eigenvalues [itex]s[/itex], and the corresponding eigenfunctions obey(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

(\Phi_s,\Phi_s') = \int \Phi_s^*(q) \, \Phi_{s'} (q)~ dq = \delta(s-s')~?

[/tex]

EDIT

For example, Hamiltonian of a free particle does not work with this, because the integral

[tex]

\int \Phi_\epsilon^*(q) \, \Phi_{\epsilon'} (q)~ dq

[/tex]

with [itex]\Phi_\epsilon(q) = e^{i \sqrt{2m\epsilon} \,q/\hbar}[/itex] does not equal to [itex]\delta(\epsilon - \epsilon')[/itex].

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# Normalization to delta distribution

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