In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands). Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules.
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves modulated by periodic functions. The theorem is named after the physicist Felix Bloch, who discovered the theorem in 1929. Mathematically, they are written where is position, is the wave function, is a periodic function with the same periodicity as the crystal, the wave vector is the crystal momentum vector, is Euler's number, and is the imaginary unit.
English is a West Germanic language in the Indo-European language family. It originated in early medieval England and, today, is the most spoken language in the world and the third most spoken native language, after Mandarin Chinese and Spanish. English is the most widely learned second language and is either the official language or one of the official languages in 59 sovereign states. There are more people who have learned English as a second language than there are native speakers.
Switzerland, officially the Swiss Confederation, is a landlocked country located at the confluence of Western, Central and Southern Europe. It is bordered by Italy to the south, France to the west, Germany to the north and Austria and Liechtenstein to the east. Switzerland is geographically divided among the Swiss Plateau, the Alps and the Jura; the Alps occupy the greater part of the territory, whereas most of the country's population of 8.7 million are concentrated on the plateau, which hosts the largest cities and economic centres, including Zürich, Geneva and Basel.
International English is the concept of using the English language as a global means of communication similar to an international auxiliary language, and often refers to the movement towards an international standard for the language. Related and sometimes synonymous terms include: Global English, World English, Common English, Continental English, General English, and Engas (English as associate language). Sometimes, these terms refer to the actuality of the situation, where English is spoken and used in numerous dialects around the world.
