Simple quantum mechanics operator question

[Chowie]

Homework Statement

What physical quantity is represented by the operator $i\bar{h}∂/∂t$

Homework Equations

$i\bar{h}∂/∂t$

The Attempt at a Solution

It's a one mark question, I just have no idea what it is and I can't find it in my notes D:.

 

[Dick]

Look at the Schrödinger equation.

 

[Chowie]

Is it total energy for a free particle?

 

[Dick]

Is it total energy for a free particle?

The Schrödinger equation applies to more than just free particles. But yes, it's the Hamiltonian. So I think it would be fair to call it the energy.

 

[Chowie]

Hmm, I have the hamiltonian written down here as

$\hat{H}=-\frac{\bar{h}^{2}}{2m}∂^{2}/∂x^{2}$


So that is also equal to $i\bar{h}∂/∂t$ ?

$\vec{}$

 

[Dick]

Hmm, I have the hamiltonian written down here as

$\hat{H}=-\frac{\bar{h}^{2}}{2m}∂^{2}/∂x^{2}$


So that is also equal to $i\bar{h}∂/∂t$ ?

$\vec{}$

That's the Hamiltonian for a free particle in one dimension. It's a special case. Your operator is the Hamiltonian even in cases where that is not the Hamiltonian.