Commutators for functions of operators (momentum/position)

Thread starter Ratpigeon
Start date May 16, 2012
Tags

Commutators Functions Operators

AI Thread Summary

The discussion focuses on proving the commutation relation [x, f(p_x)] = iħ d/d(p_x) f(p_x), where x is the position operator and p_x is the momentum operator. The initial approach involved considering the chain rule for derivatives, but the user found it challenging. Ultimately, they realized that representing the function as a power series simplified the problem. This method allowed for a clearer path to the solution. The thread highlights the importance of different mathematical techniques in solving operator commutation problems.

May 16, 2012

Ratpigeon

Homework Statement

show that [x,f(p_x)] = i \hbar d/d(p_x) f(p_x)

Homework Equations

x is the position operator in the x direction, p_x is the momentum operator; i \hbar
d/dx
[x, p_x]=xp-px

The Attempt at a Solution

I'm stuck. maybe chain rule for d/dx and d/d(p_x)...? But I don't see how I'd do it...

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May 17, 2012

Ratpigeon

Never mind - I had to reqresent it as a power series, and then it was easier

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