5. Operatoralgebra

[A, B]	=	AB - BA	(5.1)
{A, B}	=	AB + BA	(5.2)
$\displaystyle \left[\vphantom{A,B}\right.$ A, B $\displaystyle \left.\vphantom{A,B}\right]^{\dagger}_{}$	=	$\displaystyle \left[\vphantom{B^\dagger, A^\dagger}\right.$ B, A $\displaystyle \left.\vphantom{B^\dagger, A^\dagger}\right]$	(5.3)
$\displaystyle \left[\vphantom{A,B}\right.$ A, B $\displaystyle \left.\vphantom{A,B}\right]$	=	- $\displaystyle \left[\vphantom{B,A}\right.$ B, A $\displaystyle \left.\vphantom{B,A}\right]$	(5.4)
$\displaystyle \left[\vphantom{AB,C}\right.$ AB, C $\displaystyle \left.\vphantom{AB,C}\right]$	=	A[B, C] + [A, C]B	(5.5)
$\displaystyle \left[\vphantom{A,BC}\right.$ A, BC $\displaystyle \left.\vphantom{A,BC}\right]$	=	B[A, C] + [A, B]C	(5.6)
$\displaystyle \left[\vphantom{\left[A,B\right],C}\right.$ $\displaystyle \left[\vphantom{A,B}\right.$ A, B $\displaystyle \left.\vphantom{A,B}\right]$ , C $\displaystyle \left.\vphantom{\left[A,B\right],C}\right]$	=	{A,{B, C}} - {B,{A, C}}	(5.7)
$\displaystyle \left[\vphantom{AB,CD}\right.$ AB, CD $\displaystyle \left.\vphantom{AB,CD}\right]$	=	AC[B, D] + A[B, C]D + C[A, D]B + [AC]DB	(5.8)
$\displaystyle \left[\vphantom{AB,CD}\right.$ AB, CD $\displaystyle \left.\vphantom{AB,CD}\right]$	=	A{A, C}D - AC{B, D} - C{A, D}B + {C, A}DB	(5.9)
e^At	=	$\displaystyle \sum_{n=0}^{\infty}$ $\displaystyle {(At)^n \over n!}$	(5.10)
e^Ae^B	=	e^{A + B}e^{[A, B]}	(5.11)