Energy levelA quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules.
Conical combinationGiven a finite number of vectors in a real vector space, a conical combination, conical sum, or weighted sum of these vectors is a vector of the form where are non-negative real numbers. The name derives from the fact that a conical sum of vectors defines a cone (possibly in a lower-dimensional subspace). The set of all conical combinations for a given set S is called the conical hull of S and denoted cone(S) or coni(S). That is, By taking k = 0, it follows the zero vector (origin) belongs to all conical hulls (since the summation becomes an empty sum).
Solution of Schrödinger equation for a step potentialIn quantum mechanics and scattering theory, the one-dimensional step potential is an idealized system used to model incident, reflected and transmitted matter waves. The problem consists of solving the time-independent Schrödinger equation for a particle with a step-like potential in one dimension. Typically, the potential is modeled as a Heaviside step function. The time-independent Schrödinger equation for the wave function is where Ĥ is the Hamiltonian, ħ is the reduced Planck constant, m is the mass, E the energy of the particle.
Nuclear disarmamentNuclear disarmament is the act of reducing or eliminating nuclear weapons. Its end state can also be a nuclear-weapons-free world, in which nuclear weapons are completely eliminated. The term denuclearization is also used to describe the process leading to complete nuclear disarmament. Disarmament and non-proliferation treaties have been agreed upon because of the extreme danger intrinsic to nuclear war and the possession of nuclear weapons. Proponents of nuclear disarmament say that it would lessen the probability of nuclear war occurring, especially accidentally.
Affine hullIn mathematics, the affine hull or affine span of a set S in Euclidean space Rn is the smallest affine set containing S, or equivalently, the intersection of all affine sets containing S. Here, an affine set may be defined as the translation of a vector subspace. The affine hull aff(S) of S is the set of all affine combinations of elements of S, that is, The affine hull of the empty set is the empty set. The affine hull of a singleton (a set made of one single element) is the singleton itself.
