The theorem states(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{\partial E}{\partial \lambda} = \langle \psi \mid \frac{\partial H}{\partial \lambda} \mid \psi \rangle[/itex]

Where [itex]\mid \psi \rangle[/itex] is an eigenket of H.

An example (given on Wikipedia) is to find [itex]\langle \psi \mid \frac{1}{r^2} \mid \psi \rangle [/itex] for a Hydrogen eigenstate using this method with [itex]\lambda = \ell[/itex]. It is straightforward to differentiate H with respect to [itex]\ell[/itex]. However the common expression for energy only depends [itex]n[/itex]. In the Wikipedia article there is

[itex]\frac{\partial E}{\partial \ell} = \frac{\partial E}{\partial n}\frac{\partial n}{\partial \ell}[/itex].

But, how do we make sense of [itex]\frac{\partial n}{\partial \ell}[/itex]. Don't we normally (when [itex]\ell[/itex] is not varied continuously) think of [itex]n[/itex] as being somewhat independent of [itex]\ell[/itex]?

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# Feynman Hellman Theorem: dependence of E on [itex]\ell[/itex] Hydrogen

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