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Given a measurable space (,) and a measure on that space, a set in is called an atom if > and for any measurable subset , either () = or () = (). [ 1 ] The equivalence class of A {\displaystyle A} is defined by [ A ] := { B ∈ Σ : μ ( A Δ B ) = 0 } , {\displaystyle [A]:=\{B\in \Sigma :\mu (A\Delta B)=0\},} where Δ {\displaystyle \Delta ...
Illustration of the Jaynes–Cummings model. An atom in an optical cavity is shown as red dot on the top left. The energy levels of the atom that couple to the field mode within the cavity are shown in the circle on the bottom right. Transfer between the two states causes photon emission (absorption) by the atom into (out of) the cavity mode.
In the mathematical field of order theory, an element a of a partially ordered set with least element 0 is an atom if 0 < a and there is no x such that 0 < x < a. Equivalently, one may define an atom to be an element that is minimal among the non-zero elements, or alternatively an element that covers the least element 0 .
An atomic formula or atom is simply a predicate applied to a tuple of terms; that is, an atomic formula is a formula of the form P (t 1,…, t n) for P a predicate, and the t n terms. All other well-formed formulae are obtained by composing atoms with logical connectives and quantifiers. For example, the formula ∀x. P (x) ∧ ∃y. Q (y, f (x ...
The most general form of a 2×2 Hermitian matrix such as the Hamiltonian of a two-state system is given by = (+), where ,, and γ are real numbers with units of energy. The allowed energy levels of the system, namely the eigenvalues of the Hamiltonian matrix, can be found in the usual way.
In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy.Its spectrum, the system's energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system's total energy.
In the era of the old quantum theory, starting from Max Planck's proposal of quanta in his model of blackbody radiation (1900) and Albert Einstein's adaptation of the concept to explain the photoelectric effect (1905), and until Erwin Schrödinger published his eigenfunction equation in 1926, [1] the concept behind quantum numbers developed based on atomic spectroscopy and theories from ...
A graph of isotope stability, with some of the magic numbers. In nuclear physics, a magic number is a number of nucleons (either protons or neutrons, separately) such that they are arranged into complete shells within the atomic nucleus.