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QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - EXAMPLE 31.9 : When an algebraic product is defined on the space, the Lie bracket is the commutator [x,y] = xy - yx according to Lie algebra in mathematics. If [p,x] f(x) = px f(x) - xp f(x), p = -ih d / dx, find the value of [p,x] in term of i and h.
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Answer Posted / kangchuentat
QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - ANSWER 31.9 : Let [p,x] f(x) = px f(x) - xp f(x) = (-ih d / dx) x f(x) - x (-ih d / dx) f(x) = -ih { d / dx [ x f(x) ] - x d f(x) / dx } = -ih [ f(x) ] + x d f(x) / dx - x d f(x) / dx = -ih [ f(x) ]. Then [p,x] = -ih. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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