Positional Operator in k

Positional Operator in k

Progressing similarly to the derivation of a momentum operator in x (and much more succinctly),

(1)
(2)

we combine

(3)

and solve for O_x.

(4)

(5).

(6)
(7)

(8)
(9)

(10)
(11)

(12).

(13)
(14)
(15)

(16).

(17)

Ah ha,

(18)