# 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.

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