Density functional theoryDensity-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density.
Measurement in quantum mechanicsIn quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic. The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system. The formula for this calculation is known as the Born rule.
Mathematical formulation of quantum mechanicsThe mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces (L2 space mainly), and operators on these spaces.
Astronomical spectroscopyAstronomical spectroscopy is the study of astronomy using the techniques of spectroscopy to measure the spectrum of electromagnetic radiation, including visible light, ultraviolet, X-ray, infrared and radio waves that radiate from stars and other celestial objects. A stellar spectrum can reveal many properties of stars, such as their chemical composition, temperature, density, mass, distance and luminosity. Spectroscopy can show the velocity of motion towards or away from the observer by measuring the Doppler shift.
Fine structureIn atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to electron spin and relativistic corrections to the non-relativistic Schrödinger equation. It was first measured precisely for the hydrogen atom by Albert A. Michelson and Edward W. Morley in 1887, laying the basis for the theoretical treatment by Arnold Sommerfeld, introducing the fine-structure constant. The gross structure of line spectra is the line spectra predicted by the quantum mechanics of non-relativistic electrons with no spin.
ElectronThe electron (_Electron or _beta-) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ.
X-ray scattering techniquesX-ray scattering techniques are a family of non-destructive analytical techniques which reveal information about the crystal structure, chemical composition, and physical properties of materials and thin films. These techniques are based on observing the scattered intensity of an X-ray beam hitting a sample as a function of incident and scattered angle, polarization, and wavelength or energy.
Chemical compositionA chemical composition specifies the identity, arrangement, and ratio of the chemical elements making up a compound by way of chemical and atomic bonds. Chemical formulas can be used to describe the relative amounts of elements present in a compound. For example, the chemical formula for water is H2O: this means that each molecule of water is constituted by 2 atoms of hydrogen (H) and 1 atom of oxygen (O). The chemical composition of water may be interpreted as a 2:1 ratio of hydrogen atoms to oxygen atoms.
Toeplitz matrixIn linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant. For instance, the following matrix is a Toeplitz matrix: Any matrix of the form is a Toeplitz matrix. If the element of is denoted then we have A Toeplitz matrix is not necessarily square. A matrix equation of the form is called a Toeplitz system if is a Toeplitz matrix. If is an Toeplitz matrix, then the system has at-most only unique values, rather than .
AnisotropyAnisotropy (ˌaenaɪˈsɒtrəpi,_ˌænɪ-) is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example many materials exhibit very different properties when measured along different axes: physical or mechanical properties (absorbance, refractive index, conductivity, tensile strength, etc.). An example of anisotropy is light coming through a polarizer.
Static light scatteringStatic light scattering is a technique in physical chemistry that measures the intensity of the scattered light to obtain the average molecular weight Mw of a macromolecule like a polymer or a protein in solution. Measurement of the scattering intensity at many angles allows calculation of the root mean square radius, also called the radius of gyration Rg. By measuring the scattering intensity for many samples of various concentrations, the second virial coefficient, A2, can be calculated.
Relational quantum mechanicsRelational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, that is, the state is the relation between the observer and the system. This interpretation was first delineated by Carlo Rovelli in a 1994 preprint, and has since been expanded upon by a number of theorists. It is inspired by the key idea behind special relativity, that the details of an observation depend on the reference frame of the observer, and uses some ideas from Wheeler on quantum information.
