How Do You Construct the Velocity Operator?

[hellomister]

Homework Statement

I was wondering how to construct the velocity operator

Homework Equations

P=MV

The Attempt at a Solution

Since P=MV, i used the linear momentum operator and divided by M to get V. Is this the right way to construct an operator from linear momentum and position operators? I did something similar to this to construct the hamiltonian and got the hamiltonian operator. I was wondering about this because i wanted to see if linear momentum and velocity commute. I calculated that they do commute, can someone verify this?

 

[kuruman]

Yes, yes and yes. Dividing the momentum operator by m gives you the velocity operator. If an operator is a constant times another operator, the two operators commute. You may wish to prove this last result to convince yourself if you are not sure.