Spherical wave functions and certain of their properties
Spherical wave functions, Legendre and Bessel functions, and addition theorems
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Spherical wave functions, Legendre and Bessel functions, and addition theorems
Spheroidal wave functions and addition theorems
Resolving perturbed wave functions into unperturbed Hamiltonians
First order wave function in 1/Z expansion
We present the first scanning tunneling microscopy (STM) image of hydrogenic acceptor wave functions in silicon. These acceptor states appear as square-ring-like features in STM images and originate from near-surface defects introduced by high-energy bismuth implantation into a silicon (001) wafer. Scanning tunneling spectroscopy confirms the formation of a p-type surface. Effective-mass and tight-binding calculations provide an excellent description of the observed square-ring-like features, confirming their acceptor character and attributing their symmetry to the light- and heavy-hole band degeneracy in silicon. A detailed understanding of the energetic and spatial properties of acceptor wave functions in silicon is essential for engineering large-scale acceptor-based quantum devices.
Asymptotic form of wave function and threshold dependence of cross section related to electron- hydrogen ionization
For a dissipative system with Ohmic friction, we obtain a simple and exact solution for the wave function of the system plus the bath. It is described by the direct product in two independent Hilbert space. One of them is described by an effective Hamiltonian, the other represents the effect of the bath, i.e., the Brownian motion, thus clarifying the structure of the wave function of the system whose energy is dissipated by its interaction with the bath. No path integral technology is needed in this treatment. The derivation of the Weisskopf-Wigner line width theory follows easily.
Asymptotic form of wave function and threshold behavior of cross section for ionization of atomic hydrogen by electron impact
Wave functions symmetry in band theory of ferromagnetic materials, discussing fcc, bcc and hcp structures and character tables
Theoretical descriptions of the non-equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on the truncation of the expansion of the many-body wave function, (ii) compressed representations of the many-body wave function, or (iii) evolution of an effective (downfolded) representation through Green's functions. In this work, we select representative cases of each of the methods and address how these complementary approaches capture the dynamics driven by intense field perturbations to non-equilibrium states. Under strong driving, the systems are characterized by strong entanglement of the single-particle density matrix and natural populations approaching those of a strongly interacting equilibrium system. We generate a representative set of results that are numerically exact and form a basis for a critical comparison of the distinct families of methods. We demonstrate that the compressed formulation based on similarity-transformed Hamiltonians (coupled-cluster approach) is practically exact in weak fields and, hence, weakly or moderately correlated systems. Coupled cluster, however, struggles for strong driving fields, under which the system exhibits strongly correlated behavior, as measured by the von Neumann entropy of the single-particle density matrix. The dynamics predicted by Green's functions in the (widely popular) G W approximation are less accurate, but improve significantly upon the mean-field results in the strongly driven regime. Published by the American Physical Society 2025
Excited states of neutral He, obtaining wave functions from minimum principle by configuration interaction procedure
Asymptotic behavior of wave function in system of charged particles
Inelastic scattering form factors using projected Hartree-Fock wave functions
Quantum-mechanical properties derived for isolated donor atom located on surface of dielectric crystal, noting hydrogenic wave function with planar nodes
Despite their importance for exotic quantum effects, the surface electronic structure of magnetic topological insulators MnBi 2 Te 4 and MnBi 4 Te 7 remains poorly understood. Using high-efficiency spin- and angle-resolved photoemission spectroscopy, we directly image the spin-polarization and orbital character of the surface states in both compounds and map our observations onto a model wave function to describe the complex spin-orbital texture, which solidifies our understanding of the surface band structure by establishing the single-band nature of the most prominent states. Most importantly, our analysis reveals a new mechanism for reducing the magnetic gap of the topological surface states based on the orbital composition of the wave function.
Prolate spheroidal wave functions for solution of Fredholm equation for bandlimited signal detection
We apply two ab initio many-body methods based on Gutzwiller wave functions, i.e., correlation matrix renormalization theory (CMRT) and Gutzwiller conjugate gradient minimization (GCGM), to the study of crystalline phases of atomic hydrogen. Both methods avoid empirical Hubbard U parameters and are free from double-counting issues. CMRT employs a Gutzwiller-type approximation that enables efficient calculations, while GCGM goes beyond this approximation to achieve higher accuracy at higher computational cost. By benchmarking against available quantum Monte Carlo (QMC) results, we demonstrate that while both methods are more accurate than the widely used density-functional theory, GCGM systematically captures additional correlation energy missing in CMRT, leading to significantly improved total energy predictions. We also show that by including the correlation energy Ec from local density approximation in the CMRT calculation, CMRT + E c produces energy in better agreement with the QMC results in these hydrogen lattice systems.
Prolate spheroidal wave functions applied to detection Fredholm equation for band-limited noise and signals