In complex analysis, a branch of mathematics, Bloch's theorem describes the behaviour of holomorphic functions defined on the unit disk. It gives a lower...

In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves...

In complex analysis, an area of mathematics, Montel's theorem refers to one of two theorems about families of holomorphic functions. These are named after...

Blakers–Massey theorem (homotopy theory) Blaschke selection theorem (geometric topology) Bloch's theorem (complex analysis) Blondel's theorem (electric power)...

Most important works of Bloch belong to complex analysis. His early contribution is known as Bloch's theorem. This theorem asserts the existence of a...

is useful to make the Fourier series of the potential when applying Bloch's theorem. First, we may write any arbitrary position vector r {\displaystyle...

In the mathematical field of complex analysis, Nevanlinna theory is part of the theory of meromorphic functions. It was devised in 1925, by Rolf Nevanlinna...

model and the nearly-free electron model, where it is used alongside Bloch's theorem. In quantum mechanics, this approximation is often used to simplify...

such as crystals in condensed matter physics, the result is known as Bloch's theorem. Note that the solutions of the linear differential equation form a...

that depend on analysis and geometry, such as the Bloch sphere of quantum mechanics and in other branches of physics. The extended complex numbers consist...

necessarily true. A further generalization appears in the context of Bloch's theorems and Floquet theory, which govern the solution of various periodic differential...

periodic potential. The solutions in this case are known as Bloch states. Since Bloch's theorem applies only to periodic potentials, and since unceasing...

investigated including the proof of the Atiyah–Singer index theorem. The development of complex geometry was spurred on by parallel results in algebraic...

concepts originally discovered in complex analysis (such as Schwarz's theorem, Morera's theorem, the Weierstrass-Casorati theorem, Laurent series, and the classification...

In mathematics, more specifically in mathematical analysis, the Cauchy product is the discrete convolution of two infinite series. It is named after the...

multiplication in the spectral domain, consistent with the convolution theorem for Fourier transforms. With this equation for the electric field, the...

as of September 2022[update]. The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic...

Maximum power transfer theorem Norton's theorem Electric power Sheet resistance Superposition theorem Thermal noise Thévenin's theorem Uses LED-Resistor circuit...

In mathematical physics, Gleason's theorem shows that the rule one uses to calculate probabilities in quantum physics, the Born rule, can be derived from...

(2013). "An alternative proof of Wigner theorem on quantum transformations based on elementary complex analysis". Physics Letters A. 377 (39): 2709–2711...

from investigations based on these two theorems, particularly Forward Compositions Theorem, include location analysis for the limits obtained in the following...

that also follows from group representation theory as a variant of Bloch's theorem.[page needed] In particular, if a circulant Hermitian matrix is considered...

Meta-analysis is a method of synthesis of quantitative data from multiple independent studies addressing a common research question. An important part...

mathematical analysis, by allowing the use of their algebraic and topological properties for studying properties of functions. For example, all theorems of existence...

(classical analytic tools such as intermediate value theorem at the archimedean places and p-adic analysis at the nonarchimedean places) can be used. This...

economic theory needed to use functional analysis, especially convex sets and the topological fixed-point theorem, rather than the traditional differential...

analysis in the 20th century. Fundamental theorem of algebra (see History). Many incomplete or incorrect attempts were made at proving this theorem in...

and a granddaughter. “A generalization of Wiener's Tauberian theorem and harmonic analysis of rapidly increasing functions”, Proc. (Trudy) Moscow Math...

often the response becomes easier to compute. For example, in Fourier analysis, the stimulus is written as the superposition of infinitely many sinusoids...

{k} \cdot \mathbf {R} }\psi (\mathbf {r} )} This result is known as Bloch's Theorem. In the passive transformation picture, translational invariance requires...