A Deduction of the Hellmann-Feynman Theorem

On the Hellmann-Feynman theorem for statistical averages

We discuss the Hellmann-Feynman theorem for degenerate states and its application to the calculation of the derivatives of statistical averages with respect to external parameters. Some time ago there was a discussion about the validity of the HellmannFeynman theorem (HFT)[1] for degenerate states[2–5]. Recently, some of those results[3–5] proved useful in deriving an expression for the derivat...

Efficient implementation of the Hellmann-Feynman theorem in a diffusion Monte Carlo calculation.

Kinetic and potential energies of systems of (4)He atoms in the solid phase are computed at T = 0. Results at two densities of the liquid phase are presented as well. Calculations are performed by the multiweight extension to the diffusion Monte Carlo method that allows the application of the Hellmann-Feynman theorem in a robust and efficient way. This is a general method that can be applied in...

Orbit-averaged quantities, the classical Hellmann-Feynman theorem, and the magnetic flux enclosed by gyro-motion

Action integrals are often used to average a system over fast oscillations and obtain reduced dynamics. It is not surprising, then, that action integrals play a central role in the HellmannFeynman theorem of classical mechanics, which furnishes the values of certain quantities averaged over one period of rapid oscillation. This paper revisits the classical Hellmann-Feynman theorem, rederiving i...

New technique for molecular-dynamics computer simulations: Hellmann-Feynman theorem and subspace Hamiltonian approach.

Hellmann-Feynman connection for the relative Fisher information

The (i) reciprocity relations for the relative Fisher information (RFI, hereafter) and (ii) a generalized RFI-Euler theorem, are self-consistently derived from the Hellmann-Feynman theorem. These new reciprocity relations generalize the RFIEuler theorem and constitute the basis for building up a mathematical Legendre transform structure (LTS, hereafter), akin to that of thermodynamics, that und...