Half-integer

As a half-integer refers to a numerical value which is half an odd integer , z. B. In mathematical terms, such a value is an element of the set ${\displaystyle \textstyle {\frac {1}{2}},-{\frac {1}{2}},{\frac {3}{2}},-{\frac {3}{2}},\dots }$ ${\displaystyle \textstyle \left\lbrace {\frac {2n+1}{2}}\mid n\in \mathbb {Z} \right\rbrace \,.}$

In physics, the term is used in two contexts:

1. The spin quantum number of a fermion (e.g. electron ) is always positive half-integer. In the case of an atomic nucleus with an odd number of nucleons ( mass number ), the nuclear spin quantum number is also half integer. Half-integer angular momentum quantum numbers can also occur in atomic shells .
2. In connection with the interference of waves , the term “half-integer multiples of the wavelength” is sometimes used; a corresponding phase shift of two interfering waves leads to “destructive interference” (see standing wave and X-ray diffraction ).

In mathematics, the term half-integer dimension was used by Hans Maaß .

literature

• Wolfgang Nolting: Basic Course Theoretical Physics 5/2: Quantum Mechanics - Methods and Applications , Springer, 6th revised. Ed., 2006, ISBN 978-3-540-26035-6
• Richard P. Feynman : Feynman lectures on physics, 3 vol., Vol. 2, electromagnetism and structure of matter , Oldenbourg Wissensch. Vlg., 3rd edition, ISBN 978-3486255898