Homework Help: QM: Force

1. Feb 23, 2012

Niles

1. The problem statement, all variables and given/known data
Hi

In QM we define the force operator F as (in the Heisenberg picture)
$$F = \frac{1}{i\hbar}[p, H] + (d_t F)(t)$$
What I can't understand is that usually (actually, always) we write
$$F = \frac{1}{i\hbar}[p, H]$$
and neglegt the last time derivative. How can we be so certain that the force is time-independent?

Best regards,
Niles.

2. Feb 24, 2012

vela

Staff Emeritus
Shouldn't the second term be the derivative of p, not F?

3. Feb 25, 2012

Niles

You are right, it is the derivative of p. But the velocity is not necessarily time-independent?

4. Feb 25, 2012

vela

Staff Emeritus
You're looking about the derivative of the operator itself, not the derivative of the momentum of the particle. Second, ∂p/∂t ≠ 0 only if the operator has an explicit time dependence.

5. Feb 25, 2012

Niles

You are right, thanks for that. In that case it is obvious that the last term is zero.

Best regards,
Niles.