Quantum number - ryoushisuu (English spelling) quantum number

Japanese: 量子数 - りょうしすう（英語表記）quantum number

In quantum mechanics, physical quantities often have discrete values rather than continuous values. In these cases, the values of the physical quantities can be expressed using integers or half integers (an integer plus 1/2). In general, the integers or half integers that distinguish the values of physical quantities are called quantum numbers.

Since the state of a mechanical system can be distinguished by the value of its physical quantities, quantum numbers are used to represent the quantum state of a mechanical system. The motion of an electron in a hydrogen atom can be divided into radial motion and rotational motion. When an electron is treated non-relativistically, its energy has a value (- e 2 /2 a ⁰ )( 1 / n ² ) ( a ₀ is the Bohr radius ) that is inversely proportional to the square of the number n , which is determined by the number _of ripples in the state function representing the radial motion and the angular momentum l (see figure ). n is called the principal quantum number. The magnitude of the angular momentum associated with rotational motion is

(ħ is the Planck constant h divided by 2π), one of whose components is given by mħ . l is a positive integer given by l = n -1, n -2,……,0 and is called the azimuthal quantum number, and m is a positive or negative integer given by - l , - l +1,……, l and is called the magnetic quantum number. The orbital motion state of an electron is determined by simultaneously giving the three quantum numbers n , l and m . The number that indicates how many times the elementary charge the number of nucleons or the total charge of a mechanical system is is also called a quantum number.

[Hajime Tanaka]

[References] | Angular momentum | Planck constant | Bohr radius | Quantum mechanics

State function representing radial motion (Figure)
©Shogakukan ">

State function representing radial motion (Figure)

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

Japanese:

量子力学では物理量が連続的な値をとらずとびとびの値をとることが多い。この場合、物理量の値を整数または半整数（整数に1/2を加えた数）を用いて表すことができる。一般に物理量の値を区別する整数または半整数を量子数という。

　力学系の状態はその物理量の値で区別することができるので、量子数は力学系の量子的状態を表すのに用いられる。水素原子内電子の運動は、その動径方向の運動と回転運動とに分けることができる。電子を非相対論的に扱うと、そのエネルギーは、動径方向の運動を表す状態関数の波打つ数と角運動量lとで決まる数nの2乗に反比例した値(-e²/2a₀)(1/n²)（a₀はボーア半径）をもつ（図参照）。nを主量子数という。また回転運動に伴う角運動量の大きさは

（ħはプランク定数hを2πで割ったもの）で与えられ、その一成分はmħで与えられる。lはl=n-1,n-2,……,0で与えられる正整数で方位量子数、mは-l,-l+1,……,lで与えられる正負の整数で磁気量子数という。電子の軌道運動状態はn、l、mの三つの量子数を同時に与えることによって定まる。核子数や力学系の総荷電量が素電荷の何倍であるかを示す数も量子数という。