Under spherical symmetry, the irreducible representations corresponding to $L = 0, 1, 2, \cdots$ are assigned the letters $\mathrm{S}, \mathrm{P}, \mathrm{D}, \mathrm{F}, \cdots$ after which the letters progress in alphabetical order. (The familiar names of the atomic orbitals are also labelled with this sequence of letters.) Therefore, we have:
$$\mathrm{S}, \mathrm{P}, \mathrm{D}, \mathrm{F}, \mathrm{G}, \mathrm{H}, \mathrm{I}, \mathrm{K}, \cdots$$
but as far as I can tell, $\mathrm{J}$ is conspicuously omitted. I am guessing there is a reason behind this - what is it? Is it to avoid confusion with some other $J$, like the total angular momentum quantum number $J$, or is it perhaps based on some typographical argument (J being easily confused with I)?
Answer
Omitting j when alphabetically enumerating things has a long tradition.
First of all, the alphabet did not always exist in the form we know it today.
Quoting Wikipedia:
After [...] the 1st century BC, Latin adopted the Greek letters ⟨Y⟩ and ⟨Z⟩ [...] Thus it was during the classical Latin period that the Latin alphabet contained 23 letters:
[no J, V, W]
[...]
It was not until the Middle Ages that the letter ⟨W⟩ [...] was added
[...]
only after the Renaissance did the convention of treating ⟨I⟩ and ⟨U⟩ as vowels, and ⟨J⟩ and ⟨V⟩ as consonants, become established. Prior to that, the former had been merely allographs of the latter.
In some books, this has consequences till today.
The footnotes to the Confession and Catechisms [of the Presbyterian Church], containing the proof texts, are enumerated in the traditional manner, that is, by letters of the alphabet (omitting j and v, as alternative forms for i and u in the Latin alphabet). Source
But even later, long after the letters I and J were considered distinct in terms of proper spelling, their alphabetical order (I preceding J) was not firmly established.
The New General English Dictionary of 1768 had a combined section for I and J, treating both equal with respect to alphabetical order (but not regarding spelling).
Same with Handwörterbuch der allgemeinen Chemie, a German chemistry book printed in 1818.
The latest book, I could find, is the Handwörterbuch der reinen und angewandten Chemie of 1850. This is pretty close to when the letters spdefghik.. must have been defined! (Does anyone know when exactly this was?)
And now, it perfectly makes sense to me. Even if i and j were distinct letters at the time and their order should have been commonly established in the early 20th century, the possibility that some readers could still be confused about what comes first, must have lead to the decision to leave j out.
Update (2017-12)
Concerning the spelling and order of names, I was able to find evidence that is even 100 years younger.
The Berlin telephone book contained a spelling table. The first book of 1890 contained a spelling table that assigned numbers to each letter, omitting the letter J, i.e. I=9 and K=10. That is pretty similar to our orbital labels, isn't it? In the 1903 printing, words were assigned to the letters, but J was still left out. The 1905 printing was the first to include J into the spelling table. (source)
Even the Berlin address book of 1943 did not distinguish between I and J. For instance Jutta is listed before Iwanski. (Interestingly, this book doesn't even use different glyphs for I and J in the Fraktur font.)
Of course, there are many books around that time, and earlier, that sort I before J and that use different glyphs, even if printed in Fraktur (example). Nevertheless, this shows that the convention "I before J", as we know it today, was not firmly established in early 20th century Germany.
No comments:
Post a Comment