Related papers: The importance of basis states: an example using t…
We show that any short-range Hamiltonian with a gap between the ground and excited states can be written as a sum of local operators, such that the ground state is an approximate eigenvector of each operator separately. We then show that…
Finite-range numerical atomic orbitals are the basis functions of choice for several first principles methods, due to their flexibility and scalability. Generating and testing such basis sets, however, remains a significant challenge for…
In this review we consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second one is given by the…
There are few exactly solvable potentials in quantum mechanics for which the completeness relation of the energy eigenstates can be explicitly verified. In this article, we give an elementary proof that the set of bound (discrete) states…
We discuss the use of a region of uniform and constant magnetic field in order to implement a two-state atomic polarizer for an H(2S) beam. We have observed that a device with such field configuration is capable of achieving an efficient…
It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics instead of taking the electron to be a particle; we consider an electrically charged classical wave field,…
Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser…
The hydrogen molecule contains the basic ingredients to understand the chemical bond, i.e, a pair of electrons. We show a step to understand The Correspondence Principle for chaotic system in the Chemical World. The hydrogen molecule is…
The characterization of ground states among all quantum states is an important problem in quantum many-body physics. For example, the celebrated entanglement area law for gapped Hamiltonians has allowed for efficient simulation of 1d and…
A core level of basic information for physics is identified, based on an analysis of the characteristics of the parameters space, time, mass and charge. At this level, it is found that certain symmetries operate, which can be used to…
A new model of quantum mechanics, Classical Quantum Mechanics, is based on the (nearly heretical) postulate that electrons are physical objects that obey classical physical laws. Indeed, ionization energies, excitation energies etc. are…
Reduced basis methods provide a powerful framework for building efficient and accurate emulators. Although widely applied in many fields to simplify complex models, reduced basis methods have only been recently introduced into nuclear…
It is well known that density matrices can be used in quantum mechanics to represent the information available to an observer about either a system with a random wave function (``statistical mixture'') or a system that is entangled with…
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…
An effective Hamiltonian is considered for hydrogen bonding between two molecules due to the quantum mechanical interaction between the orbitals of the H-atom and the donor and acceptor atoms in the molecules. The Hamiltonian acts on two…
Expectation values of powers of the radial coordinate in arbitrary hydrogen states are given, in the quantum case, by an integral involving the associated Laguerre function. The method of brackets is used to evaluate the integral in…
Knowledge of the ground state of a homogeneous quantum many-body system can be used to find the exact ground state of a dual inhomogeneous system with a confining potential. For the complete family of parent Hamiltonians with a ground state…
The hydrogen atom as relativistic bound-state system of a proton and an electron in the complex-mass scheme is investigated. Interaction of a proton and an electron in the atom is described by the Lorentz-scalar Coulomb potential; the…
Homogeneous electron and nuclear gases are transformed to a localized trial density in absolute coordinates of the multi-component hamiltonian to determine the stability of forming bound states. Regions of stability were found both at the…
We leverage the power of neural quantum states to describe the ground state wave function of solid and liquid atomic hydrogen, including both electronic and protonic degrees of freedom. For static protons, the resulting Born-Oppenheimer…