If [A, B] = 1 then [A, A + B] = 1
[A, A + B] = A(A + B) - (A + B)A = AA + AB - AA - BA = AB - BA = [A, B] = 1
We have p = c(A + B) and [x, p] = iħ.
xp - px = iħ
cx(A + B) - c(A + B)x = iħ
x(A + B) - (A + B)x = iħ/c | multiply on A from the left
Ax(A + B) - A(A + B)x = iħ/c A | A(A + B)...
Homework Statement
Find the operator for position x if the operator for momentum p is taken to be \left(\hbar/2m\right)^{1/2}\left(A + B\right), with \left[A,B\right] = 1 and all other commutators zero.
Homework Equations
Canonical commutation relation
\left [ \hat{ x }, \hat{ p } \right ] =...