磁気量子数

WordNet

give numbers to; "You should number the pages of the thesis"
place a limit on the number of (同)keep_down
a concept of quantity involving zero and units; "every number has a unique position in the sequence"
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" (同)figure
a clothing measurement; "a number 13 shoe"
an item of merchandise offered for sale; "she preferred the black nylon number"; "this sweater is an all-wool number"
a numeral or string of numerals that is used for identification; "she refused to give them her Social Security number" (同)identification number
a select company of people; "I hope to become one of their number before I die"
the grammatical category for the forms of nouns and pronouns and verbs that are used depending on the number of entities involved (singular or dual or plural); "in English the subject and the verb must agree in number"
enumerate; "We must number the names of the great mathematicians" (同)list
of or relating to or caused by magnetism; "magnetic forces"
having the properties of a magnet; i.e. of attracting iron or steel; "the hard disk is covered with a thin coat of magnetic material" (同)magnetized, magnetised
capable of being magnetized
determined by earths magnetic fields; "magnetic north"; "the needle of a magnetic compass points to the magnetic north pole"
so frightened as to be unable to move; stunned or paralyzed with terror; petrified; "too numb with fear to move"
make numb or insensitive; "The shock numbed her senses" (同)benumb, blunt, dull
(physics) the smallest discrete quantity of some physical property that a system can possess (according to quantum theory)
a discrete amount of something that is analogous to the quantities in quantum theory
(physics) a device that attracts iron and produces a magnetic field

PrepTutorEJDIC

〈U〉〈C〉(数えて得られる)『数,数量』 / 〈C〉(概念としての)『数,数字』 / 〈C〉『番号』 / 〈C〉(演奏会や演劇の)番組,出し物;曲目 / 〈C〉(雑誌の)号 / 〈U〉(文法で)数(すう) / 《複数形で》数の上の優勢 / 《複数形で》算数 / 〈C〉《単数形で》《話》(商品としての)洋服の1点;商品,売り物 / 〈C〉《単随形で》《俗》女の子 / …‘を'数える / (…の中に,…として)…‘を'含める,加える《+『among』(『with, as』)+『名』》 / …‘に'番号をつける / …‘の'数となる / 《しばしば受動態で》…‘の'数を制限する / 総計(…に)なる《+『in』+『名』〈数〉》
磁石の;磁気の(による,を帯びた) / 人を引き付ける,魅力のある
麻痺(まひ)した,感覚を失った,しびれた / …‘の'感覚を失わせる,‘を'しびれさせる
量子
『磁石』 / (魅力などで)(人の注意などを)引く人(もの)《+『of』+『名』》;(…にとって)魅力的な場所(もの)《+『to』(『for』)+『名』》

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2014/07/24 21:24:26」(JST)

wiki en

In atomic physics, the magnetic quantum number is the third of a set of quantum numbers (the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) which describe the unique quantum state of an electron and is designated by the letter m. The magnetic quantum number denotes the energy levels available within a subshell.

Derivation

There is a set of quantum numbers associated with the energy states of the atom. The four quantum numbers n, ℓ, m, and s specify the complete and unique quantum state of a single electron in an atom called its wavefunction or orbital. The wavefunction of the Schrödinger wave equation reduces to the three equations that when solved lead to the first three quantum numbers. Therefore, the equations for the first three quantum numbers are all interrelated. The magnetic quantum number arose in the solution of the azimuthal part of the wave equation as shown below.

The magnetic quantum number associated with the quantum state is designated as m. The quantum number m refers, loosely, to the direction of the angular momentum vector. The magnetic quantum number m only affects the electron's energy if it is in a magnetic field because in the absence of one, all spherical harmonics corresponding to the different arbitrary values of m are equivalent. "M" also affects the probability cloud^[why?]. Given a particular ℓ, m is entitled to be any integer from -ℓ up to ℓ. More precisely, for a given orbital momentum quantum number ℓ (representing the azimuthal quantum number associated with angular momentum), there are 2ℓ+1 integral magnetic quantum numbers m ranging from -ℓ to ℓ, which restrict the fraction of the total angular momentum along the quantization axis so that they are limited to the values m. This phenomenon is known as space quantization. It was first demonstrated by two German physicists, Otto Stern and Walther Gerlach. Since each electronic orbit has a magnetic moment in a magnetic field the electronic orbit will be subject to a torque which tends to make the vector parallel to the field. The precession of the electronic orbit in a magnetic field is called the Larmor precession.

To describe the magnetic quantum number m you begin with an atomic electron's angular momentum, L, which is related to its quantum number ℓ by the following equation:

where is the reduced Planck constant. The energy of any wave is the frequency multiplied by Planck's constant. This causes the wave to display particle-like packets of energy called quanta. To show each of the quantum numbers in the quantum state, the formulae for each quantum number include Planck's reduced constant which only allows particular or discrete or quantized energy levels.

To show that only certain discrete amounts of angular momentum are allowed, ℓ has to be an integer. The quantum number m refers to the projection of the angular momentum for any given direction, conventionally called the z direction. L_z, the component of angular momentum in the z direction, is given by the formula:

Another way of stating the formula for the magnetic quantum number is the eigenvalue, J_z=m_ℓh/2π.

Where the quantum number ℓ is the subshell, the magnetic number m represents the number of possible values for available energy levels of that subshell as shown in the table below.

Relationship between Quantum Numbers
Orbital	Values	Number of Values for m
s		1
p		3
d		5
f		7
g		9

The magnetic quantum number determines the energy shift of an atomic orbital due to an external magnetic field, hence the name magnetic quantum number (Zeeman effect).

However, the actual magnetic dipole moment of an electron in an atomic orbital arrives not only from the electron angular momentum, but also from the electron spin, expressed in the spin quantum number.

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