Symmetry in quantum mechanicsSymmetries in quantum mechanics describe features of spacetime and particles which are unchanged under some transformation, in the context of quantum mechanics, relativistic quantum mechanics and quantum field theory, and with applications in the mathematical formulation of the standard model and condensed matter physics. In general, symmetry in physics, invariance, and conservation laws, are fundamentally important constraints for formulating physical theories and models.
Linear algebraLinear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.
Stellar astronomyA star is an astronomical object comprising a luminous spheroid of plasma held together by self-gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night; their immense distances from Earth make them appear as fixed points of light. The most prominent stars have been categorised into constellations and asterisms, and many of the brightest stars have proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations.
Statistical mechanicsIn physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, chemistry, and neuroscience.
Topics in electromagnetismIn physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electrostatics and magnetism, two distinct but closely intertwined phenomena.
Interpretations of quantum mechanicsAn interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraordinarily broad range of experiments, there exist a number of contending schools of thought over their interpretation. These views on interpretation differ on such fundamental questions as whether quantum mechanics is deterministic or stochastic, local or non-local, which elements of quantum mechanics can be considered real, and what the nature of measurement is, among other matters.
Topics in nanotechnologyNanotechnology, often shortened to nanotech, is the use of matter on atomic, molecular, and supramolecular scales for industrial purposes. The earliest, widespread description of nanotechnology referred to the particular technological goal of precisely manipulating atoms and molecules for fabrication of macroscale products, also now referred to as molecular nanotechnology. A more generalized description of nanotechnology was subsequently established by the National Nanotechnology Initiative, which defined nanotechnology as the manipulation of matter with at least one dimension sized from 1 to 100 nanometers (nm).
Quantum opticsQuantum optics is a branch of atomic, molecular, and optical physics dealing with how individual quanta of light, known as photons, interact with atoms and molecules. It includes the study of the particle-like properties of photons. Photons have been used to test many of the counter-intuitive predictions of quantum mechanics, such as entanglement and teleportation, and are a useful resource for quantum information processing. Light propagating in a restricted volume of space has its energy and momentum quantized according to an integer number of particles known as photons.
Topics in organic chemistryOrganic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms. Study of structure determines their structural formula. Study of properties includes physical and chemical properties, and evaluation of chemical reactivity to understand their behavior.
Stellar nucleosynthesisStellar nucleosynthesis is the creation (nucleosynthesis) of chemical elements by nuclear fusion reactions within stars. Stellar nucleosynthesis has occurred since the original creation of hydrogen, helium and lithium during the Big Bang. As a predictive theory, it yields accurate estimates of the observed abundances of the elements. It explains why the observed abundances of elements change over time and why some elements and their isotopes are much more abundant than others.
