Bracket Notation in Quantum Mechanics
55
There are some notational conveniences. For example, the inner bracket is written
conventionally as
w · v = =w|v,
(3.99)
which means that the inner product is regarded as the “product of the matrices,”
w · v =
w 1 , w 2 , · · ·
⎛
⎜
⎝
v 1
v 2
. . .
⎞
⎟
⎠ .
(3.100)
Also in the main text we have had
|vw|
(3.101)
and also this can be regarded as a “matrix,” made by a matrix product,
|vw| =
⎛
⎜
⎝
v 1
v 2
. . .
⎞
⎟
⎠
w 1 , w 2 , · · ·
=
⎛
⎝
v 1 w 1 v 1 w 2 · · ·
v 2 w 1 v 2 w 2 · · ·
. . .
⎞
⎠ .
(3.102)