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8.4: Quantum forces - the Hellmann-Feynman Theorem
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/08%3A_The_Variational_Principle/8.04%3A_Quantum_forces_-_the_Hellmann-Feynman_Theorum
$\frac{dE}{d\alpha} = \langle \frac{d\phi}{ d\alpha} |\hat{H} |\phi \rangle + \langle \phi | \frac{d\hat{H}}{d\alpha} |\phi \rangle + \langle \phi |\hat{H} | \phi \rangle \nonumber$ \[\frac{dE}{d\al... $\frac{dE}{d\alpha} = \langle \frac{d\phi}{ d\alpha} |\hat{H} |\phi \rangle + \langle \phi | \frac{d\hat{H}}{d\alpha} |\phi \rangle + \langle \phi |\hat{H} | \phi \rangle \nonumber$ $\frac{dE}{d\alpha} = \langle \phi | \frac{d\hat{H}}{ d\alpha} |\phi \rangle + E \frac{d}{d\alpha} \langle \phi | \phi \rangle + \langle \phi | \frac{d\hat{H}}{d\alpha} | \phi \rangle \nonumber$

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