Hellmann-Feynman theorem in curvilinear coordinate systems.
Hellmann-Feynman theorem in curvilinear coordinates for exact and for floating variational wave functions
COORDINATE SYSTEM↗
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Electrostatic Hellmann-Feynman theorem applied to long-range interatomic forces - The hydrogen molecule.
The use of the electrostatic Hellmann-Feynman theorem for the calculation of the leading term in the 1/R expansion of the force of interaction between two well-separated hydrogen atoms is discussed. Previous work has suggested that whereas this term is determined wholly by the first-order wavefunction when calculated by perturbation theory, the use of the Hellmann-Feynman theorem apparently requires the wavefunction through second order. It is shown how the two results may be reconciled and that the Hellmann-Feynman theorem may be reformulated in such a way that only the first-order wavefunction is required.
Steiner, E.↗
Time-dependent Hellmann-Feynman theorems for variational wavefunctions.
Conditions under which optimal wave functions satisfy various time-dependent Hellmann-Feynman theorems
HELLMANN-FEYNMAN THEOREM↗
Electrostatic Hellmann-Feynman theorem applied to the long-range interaction of two hydrogen atoms.
Long range interaction of two H atoms calculated with electrostatic Hellmann-Feynman theorem, determining part of second order molecular wave function
ELECTROMAGNETIC INTERACTION↗
Hypervirial theorems and the hellmann- feynman theorem in different coordinate systems.
Hypervirial theorems and Hellmann-Feynman theorem in different coordinate systems
VIRIAL THEOREM↗
Hypervirial Theorems and the Hellman- Feynman Theorem in Different Coordinate Systems
Hypervirial and Hellmann-Feynman theorems in different coordinate systems
COORDINATE SYSTEM↗
Demonstration of the rodeo algorithm on a quantum computer
The rodeo algorithm is an efficient algorithm for eigenstate preparation and eigenvalue estimation for any observable on a quantum computer. This makes it a promising tool for studying the spectrum and structure of atomic nuclei as well as other fields of quantum many-body physics. The only requirement is that the initial state has sufficient overlap probability with the desired eigenstate. While it is exponentially faster than well-known algorithms such as phase estimation and adiabatic evolution for eigenstate preparation, it has yet to be implemented on an actual quantum device. In this work, we apply the rodeo algorithm to determine the energy levels of a random one-qubit Hamiltonian, resulting in a relative error of 0.08% using mid-circuit measurements on the IBM Q device Casablanca. This surpasses the accuracy of directly-prepared eigenvector expectation values using the same quantum device. We take advantage of the high-accuracy energy determination and use the Hellmann-Feynman theorem to compute eigenvector expectation values for a different random one-qubit observable. For the Hellmann-Feynman calculations, we find a relative error of 0.7%. Here, we conclude by discussing possible future applications of the rodeo algorithm for multi-qubit Hamiltonians.
algorithm↗
Time-dependent hypervirial theorems and the like for variational wave functions
Time dependent hypervirial theorem for variational wave functions - variational calculus
VIRIAL THEOREM↗
Interatomic forces at very short range.
Electronic energy of interacting atoms at short range, noting Hellman-Feynman theorem for electron density in elliptic coordinates
HELLMANN-FEYNMAN THEOREM↗
The Internuclear Separation Derivatives of the Energy of a Diatomic Molecule
Hellman-Feynman theorem used for internuclear separation derivatives of diatomic molecule energy
NUCLEAR INTERACTION↗
The nature of intermolecular forces.
Intermolecular forces theory, considering hydrogen atom interaction through Born- Oppenheimer approximation and variational calculations
ATOMIC COLLISION↗
New force theorem.
New force theorem for determining molecular energy derivatives with respect to internuclear distance derived from Hellmann-Feynman expression
MOLECULAR ENERGY↗