Sphalerons in an SU(2) model with one Higgs doublet and one scalar singlet

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

sp3d and sp3d 2 Hybridization

Molecular Orbital Energy Diagrams

Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...

In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the shear...