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terp.asessed
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Homework Statement
I am practicing problems from the textbook, but have no idea how to get to some of the solutions available in the back of the textbook...
6-16. Evaluate the commutator [C,D] where C and D are given below:
(e) C = d2/dx2, D = x
(g) C = integral (x = 0 to infinite) dx, D = d/dx
Homework Equations
[C,D] = CD - DC
The Attempt at a Solution
e)
CDf(x) = C(xf(x)) = d2xf(x)/dx2 = 0 + xd2f(x)/dx2
DCf(x) = D(d2f(x)/dx2) =xd2f(x)/dx2
[C,D] = xd2f(x)/dx2 - xd2f(x)/dx2 is what I got, but the solution, according to the textbook is:
[C,D] = 2df(x)/dx...how do I get to here?
g)
CDf(x) = C(df(x)/dx) = integral (x=0 to infinite) df(x)/dx * dx = f(x) (integration from x = 0 to infinite)
DCf(x) = D(integral f(x)) = d/dx integral f(x)*dx...which is what? I am lost here...
Again, for this part, the solution is:
[C,D]f(x) = -f(0)...could someone explain how this value was hinted?