Antisymmetrizer, the Glossary

Table of Contents

1. 23 relations: Associative property, Atomic orbital, Character theory, Coset, Cyclic permutation, Electron, Fermion, Identity function, Indistinguishable particles, Intermolecular force, Laplace expansion, Leibniz formula for determinants, Parity of a permutation, Pauli exclusion principle, Permutation, Projection (linear algebra), Quantum mechanics, Representation theory, Slater determinant, Spin (physics), Subgroup, Symmetric group, Unitary operator.

2. Determinants
3. Pauli exclusion principle

Associative property

In mathematics, the associative property is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result.

See Antisymmetrizer and Associative property

Atomic orbital

In quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. Antisymmetrizer and atomic orbital are quantum chemistry.

See Antisymmetrizer and Atomic orbital

Character theory

In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix.

See Antisymmetrizer and Character theory

Coset

In mathematics, specifically group theory, a subgroup of a group may be used to decompose the underlying set of into disjoint, equal-size subsets called cosets.

See Antisymmetrizer and Coset

Cyclic permutation

In mathematics, and in particular in group theory, a cyclic permutation is a permutation consisting of a single cycle. Antisymmetrizer and cyclic permutation are permutations.

See Antisymmetrizer and Cyclic permutation

Electron

The electron (or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge.

See Antisymmetrizer and Electron

Fermion

In particle physics, a fermion is a particle that follows Fermi–Dirac statistics.

See Antisymmetrizer and Fermion

Identity function

Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value that was used as its argument, unchanged.

See Antisymmetrizer and Identity function

Indistinguishable particles

In quantum mechanics, indistinguishable particles (also called identical or indiscernible particles) are particles that cannot be distinguished from one another, even in principle. Antisymmetrizer and indistinguishable particles are Pauli exclusion principle.

See Antisymmetrizer and Indistinguishable particles

Intermolecular force

An intermolecular force (IMF) (or secondary force) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles, e.g. atoms or ions.

See Antisymmetrizer and Intermolecular force

Laplace expansion

In linear algebra, the Laplace expansion, named after Pierre-Simon Laplace, also called cofactor expansion, is an expression of the determinant of an -matrix as a weighted sum of minors, which are the determinants of some -submatrices of. Antisymmetrizer and Laplace expansion are determinants.

See Antisymmetrizer and Laplace expansion

Leibniz formula for determinants

In algebra, the Leibniz formula, named in honor of Gottfried Leibniz, expresses the determinant of a square matrix in terms of permutations of the matrix elements. Antisymmetrizer and Leibniz formula for determinants are determinants.

See Antisymmetrizer and Leibniz formula for determinants

Parity of a permutation

In mathematics, when X is a finite set with at least two elements, the permutations of X (i.e. the bijective functions from X to X) fall into two classes of equal size: the even permutations and the odd permutations. Antisymmetrizer and Parity of a permutation are permutations.

See Antisymmetrizer and Parity of a permutation

Pauli exclusion principle

In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that obeys the laws of quantum mechanics. Antisymmetrizer and Pauli exclusion principle are quantum mechanics.

See Antisymmetrizer and Pauli exclusion principle

Permutation

In mathematics, a permutation of a set can mean one of two different things. Antisymmetrizer and permutation are permutations.

See Antisymmetrizer and Permutation

Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself (an endomorphism) such that P\circ P.

See Antisymmetrizer and Projection (linear algebra)

Quantum mechanics

Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms.

See Antisymmetrizer and Quantum mechanics

Representation theory

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.

See Antisymmetrizer and Representation theory

Slater determinant

In quantum mechanics, a Slater determinant is an expression that describes the wave function of a multi-fermionic system. Antisymmetrizer and Slater determinant are determinants, Pauli exclusion principle, quantum chemistry and quantum mechanics.

See Antisymmetrizer and Slater determinant

Spin (physics)

Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms.

See Antisymmetrizer and Spin (physics)

Subgroup

In group theory, a branch of mathematics, given a group under a binary operation ∗, a subset of is called a subgroup of if also forms a group under the operation ∗.

See Antisymmetrizer and Subgroup

Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

See Antisymmetrizer and Symmetric group

Unitary operator

In functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product.

See Antisymmetrizer and Unitary operator

See also

Determinants

• Alternant matrix
• Antisymmetrizer
• Bareiss algorithm
• Berezinian
• Capelli's identity
• Cauchy matrix
• Cauchy–Binet formula
• Cayley–Menger determinant
• Circulant matrix
• Cramer's rule
• Cross Gramian
• Determinant
• Determinantal conjecture
• Dieudonné determinant
• Discriminant
• Distance geometry
• Dodgson condensation
• Faddeev–LeVerrier algorithm
• Fischer's inequality
• Fredholm determinant
• Frobenius determinant theorem
• Functional determinant
• Gram matrix
• Grothendieck trace theorem
• Hadamard's inequality
• Hilbert matrix
• Hurwitz determinant
• Invertible matrix
• Jacobi's formula
• Jacobian matrix and determinant
• Laplace expansion
• Leibniz formula for determinants
• Maillet's determinant
• Minor (linear algebra)
• Moore matrix
• Persymmetric matrix
• Pfaffian
• Quasideterminant
• Resultant
• Rule of Sarrus
• Slater determinant
• Sylvester's determinant identity
• Totally positive matrix
• Vandermonde matrix
• Volume form
• Weinstein–Aronszajn identity
• Wronskian

Pauli exclusion principle

• Antisymmetrizer
• Electron degeneracy pressure
• Exchange interaction
• Indistinguishable particles
• Pauli exclusion principle
• Slater determinant
• Symmetry in quantum mechanics
• VIP2 experiment

References

[1] https://en.wikipedia.org/wiki/Antisymmetrizer

Also known as Antisymmetrization operator, Antisymmetrizing operator.