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单词 multiplicity
释义

multiplicity


mul·ti·plic·i·ty

M0478400 (mŭl′tə-plĭs′ĭ-tē)n. pl. mul·ti·plic·i·ties 1. The state of being various or manifold: the multiplicity of architectural styles on that street.2. A large number: a multiplicity of ideas.
[Middle English, from Old French multiplicite, from Late Latin multiplicitās, from multiplex, various; see multiplex.]
mul′ti·plic′i·tous adj.

multiplicity

(ˌmʌltɪˈplɪsɪtɪ) n, pl -ties1. a large number or great variety2. the state of being multiple3. (General Physics) physics a. the number of levels into which the energy of an atom, molecule, or nucleus splits as a result of coupling between orbital angular momentum and spin angular momentumb. the number of elementary particles in a multiplet

mul•ti•plic•i•ty

(ˌmʌl təˈplɪs ɪ ti)

n., pl. -ties. 1. a large number. 2. the state of being multiplex or manifold; manifold variety. [1580–90; < Late Latin multiplicitās= Latin multiplic- multiplex + -itās -ity]
Thesaurus
Noun1.multiplicity - the property of being multiplemagnitude - the property of relative size or extent (whether large or small); "they tried to predict the magnitude of the explosion"; "about the magnitude of a small pea"
2.multiplicity - a large numbernumerosity, numerousnessnumber, figure - the property possessed by a sum or total or indefinite quantity of units or individuals; "he had a number of chores to do"; "the number of parameters is small"; "the figure was about a thousand"multitudinousness - a very large number (especially of people)

multiplicity

noun number, lot, host, mass, variety, load (informal), pile (informal), ton, stack, diversity, heap (informal), array, abundance, myriad, profusion a writer who uses a multiplicity of styles

multiplicity

noun1. The quality of being made of many different elements, forms, kinds, or individuals:diverseness, diversification, diversity, heterogeneity, heterogeneousness, miscellaneousness, multifariousness, multiformity, variegation, variety, variousness.Biology: polymorphism.2. An indeterminately great amount or number:jillion, million (often used in plural), ream, trillion.Informal: bushel, gob (often used in plural), heap (often used in plural), load (often used in plural), lot, oodles, passel, peck, scad (often used in plural), slew, wad, zillion.
Translations
Vielzahlmolteplicit...molteplicità

multiplicity


multiplicity

Physics the number of levels into which the energy of an atom, molecule, or nucleus splits as a result of coupling between orbital angular momentum and spin angular momentum

Multiplicity

 

the number of possible spatial orientations of the total spin of an atom or molecule. According to quantum mechanics, multiplicity κ is equal to 2S + 1, where S is the spin quantum number. For systems with an odd number N of electrons, 5 = 1/2, 3/2, 5/2, . . . , and the multiplicity is even (κ = 2,4, 6,. . . ). Quantum states such as doublets, quartets, and sextets are possible &>r them. If N is even, then S = 0, 1, 2, . . ., and the multiplicity is odd (κ = 1, 3, 5,. . . ), and singlet, triplet, quintet, and other odd states are possible. For example, for systems with one electron (the H atom, the He+ ion; S = 1/2, κ = 2), only doublet states occur; for systems with two electrons (the He atom and the H2 molecule), singlet states (S = 0, κ = 1; the spins of the electrons are antiparallel) and triplet states (S = 1, κ = 3; the electron spins are parallel) occur. For N electrons the maximum multiplicity (κ = N + 1) corresponds to parallel orientation of their spins.

The multiplicity determines the degree of degeneracy of the levels of the atom or molecule. The 25 + 1 quantum states that correspond to an energy level with a given S differ in the values of the projection of the total spin and are characterized by the quantum number Ms = S, S— 1,. . ., —S, which determines the magnitude of the projection. As a result of spin-orbital interaction, an energy level may split into κ = 2S + 1 sublevels (multiplet splitting, which leads to the splitting of spectral lines).

The values of multiplicity for the quantum states of atoms and molecules are determined by the electrons in open shells, since electron spins are compensated in closed shells. For the energy levels of alkali metals with one outer electron, κ = 2, just as for the H atom; for the energy levels of complex atoms with filling p-, d-, and f- shells, the multiplicity may be high (up to 11). Multiplicities of κ = 1 for the ground level and κ = 1 and 3 for excited energy levels are characteristic of chemically stable molecules, which usually have an even number of electrons. For free radicals with one electron with uncompensated spin, a multiplicity of κ = 2 is typical.

M. A. EL’IASHEVICH

multiplicity

[‚məl·tə′plis·əd·ē] (mathematics) A root of a polynomial ƒ(x) has multiplicity n if (x - a) n is a factor of ƒ(x) and n is the largest possible integer for which this is true. The geometric multiplicity of an eigenvalue λ of a linear transformation T is the dimension of the null space of the transformation T - λ I, where I denotes the identity transformation. The algebraic multiplicity of an eigenvalue λ of a linear transformation T on a finite-dimensional vector space is the multiplicity of λ as a root of the characteristic polynomial of T. (physics) In a system having Russell-Saunders coupling, the quantity 2 S +1, where S is the total spin quantum number.

multiplicity


  • noun

Synonyms for multiplicity

noun number

Synonyms

  • number
  • lot
  • host
  • mass
  • variety
  • load
  • pile
  • ton
  • stack
  • diversity
  • heap
  • array
  • abundance
  • myriad
  • profusion

Synonyms for multiplicity

noun the quality of being made of many different elements, forms, kinds, or individuals

Synonyms

  • diverseness
  • diversification
  • diversity
  • heterogeneity
  • heterogeneousness
  • miscellaneousness
  • multifariousness
  • multiformity
  • variegation
  • variety
  • variousness
  • polymorphism

noun an indeterminately great amount or number

Synonyms

  • jillion
  • million
  • ream
  • trillion
  • bushel
  • gob
  • heap
  • load
  • lot
  • oodles
  • passel
  • peck
  • scad
  • slew
  • wad
  • zillion

Synonyms for multiplicity

noun the property of being multiple

Related Words

  • magnitude

noun a large number

Synonyms

  • numerosity
  • numerousness

Related Words

  • number
  • figure
  • multitudinousness
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更新时间:2025/2/24 0:08:56