What is the Commutator of [x, p e^(-p)]?

[Prins]

Homework Statement

commutator of [x,p e^(-p) ]

Homework Equations

The Attempt at a Solution

answer is i - i.e^(-p)

 

[blue_leaf77]

what is p in the e^(-p)?

 

[ensign_nemo]

If it's the usual notation for quantum mechanics, x is position and p is momentum.

 

[henil]

its just the usual commutation relation of x and p with e^(-p) in multiplication.
the method of solving remains the same.

 

[blue_leaf77]

I will assume that the multiplicative factor which should exist next to the momentum in the exponential in order to conform with the dimensionality is presumed to be unity. There is a shortcut formula for calculating commutators of the form [x,f(p)] and [p,g(x)]. In case you never heard about it, you should then do the calculation by first expanding $e^{-p}$ into power series and use the fundamental commutation relation between x and p.

 

[berkeman]

Homework Statement

commutator of [x,p e^(-p) ]

Homework Equations

The Attempt at a Solution

answer is i - i.e^(-p)

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