More explicitly, p ^ ^ is a vector operator (i.e. a vector consisting of three operators ( p ^ ^ x , p ^ ^ y , p ^ ^ z ) ), defined by: p ^ ^ x = i ℏ ℏ lim a → → 0 T ^ ^ ( a x ^ ^ ) − − I ^ ^ a where I ^ ^ is the identity operator and x ^ ^ is the unit vector in the x -direction. ( p ^ ^ y , p ^ ^ z are defined analogously.)