My professor's solution is as follows:
It relies on the identity
\begin{align*}
[\partial f(x,y)/\partial x] &= [\partial f(y)/\partial x]*[\partial f(x)/\partial x]
\end{align*}
to get from the penultimate line to the last line, however this is an identity I am neither familiar nor comfortable...
The problem was delivered exactly as phrased in the "Homework Statement":
"Evaluate the commutator [𝑥(𝜕/𝜕𝑦), 𝑦(𝜕/𝜕𝑥)] by applying the operators to an arbitrary
function 𝑓(𝑥,𝑦)."
That feeling that you're missing something? That's exactly where I've been all day...
I checked a specific function, but I picked the function f(x) = x^2 +y^2, and my prof replied that "that's not a single valued function so it won't work, remember the postulates!"
But even when I plug in single valued functions s.a. y=x-x^3, the commutator is not 0...
My professor's solution...
Hello,
In QM class this morning my Prof claimed that the commutator [𝑥(𝜕/𝜕𝑦), 𝑦(𝜕/𝜕𝑥)] = 0.
However, my classmate and I arrived at x(d/dx) - y(d/dy).
Can someone explain how (or if) our professor is correct?