- #1
widderjoos
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Homework Statement
Suppose we had an operator A that multiplied a vector by it's norm:
[itex]A \mid \psi \rangle = \langle \psi \mid \psi \rangle \mid \psi \rangle[/itex]
I wanted to know what it's commutator with a constant would be.
Homework Equations
[itex]\left[A,B\right] = AB - BA[/itex]
The Attempt at a Solution
Suppose b is a real number greater than 1, then
[itex]\left[A,b\right] \mid \psi \rangle =(Ab-bA)\mid \psi \rangle [/itex]
[itex]=A (b\mid \psi \rangle ) - b (A \mid \psi \rangle ) = (b^2 - b)\langle \psi \mid \psi \rangle \mid \psi \rangle[/itex]
I'm think the second equality is wrong since I read that the commutator of an operator with a constant should be 0 and the operator A looks nonlinear. But what should be done instead? Thanks