Bracket notation is writing different brackets, surrounding single unit, including
for bra vectors and
for ket vectors.
Unfortunately, I see no such template in OneNote math:

Bracket notation is writing different brackets, surrounding single unit, including
for bra vectors and
for ket vectors.
Unfortunately, I see no such template in OneNote math:

Using the equation editor just type:
\bra|
followed by a space, for the bra vector brackets and:
|\ket
followed by a space, for the ket vector brackets.
For the full bra-ket inner product notation type:
\bra|\ket
followed by a space. To insert space for operators right-click on the bracket and select 'insert argument before/after" to separate the bracket into 2 or more parts
To do it just use the single bracket list as shown in the picture and select from it the relevant large < or > (far right of first row in pic). Then use shift forward slash (the button next to left-shift on most keyboards) to give the vertical line |. In combination you get correct bra-ket notation.
(For OneNote 2016, not sure for other versions) You can write \bra and get the < , and write \ket and get the > (And it looks just like it would in LaTeX)
You can use encapsulation. For example if you want to create a "ket" operator, use the |-template first and then include the >-template into it. It might not be as perfect as in TeX, but the tops and bottoms of the brackets align.