## Hamiltonian

$H_{\psi }=E_{\psi }$

1-D: $E_{TOTAL}\psi (x)=E_{k}\psi (x)+V(x)\psi(x)=-\frac{h^{2}}{8\pi ^{2}m}\frac{d^{2}\psi(x)}{dx^{2}}+V(x)\psi(x)$

Alexandra Salata 1J
Posts: 41
Joined: Wed Sep 30, 2020 9:39 pm

### Hamiltonian

I've seen quite a few topics on the Schrodinger's equation and I understand what all the elements represent... apart from H(Hamiltonian). I have no idea as to what it does even after reading the textbook and watching Dr Lavelle's lecture. Anyone have any easy and straightforward explanations for it?

tamara masri_3D
Posts: 40
Joined: Wed Sep 30, 2020 9:35 pm
Been upvoted: 1 time

### Re: Hamiltonian

Hi, I'm not sure if this will be much help, but I understood that the Hamiltonian variable was essentially representing some math function being applied to the wave function. In his lecture, Professor Lavelle said this was originally just the double derivative of the wave function, but now we know there are other ways to get the same result (which he didn't elaborate on so I assume we don't need to know that:)

Mikayla Kwok 3L
Posts: 42
Joined: Wed Sep 30, 2020 9:51 pm

### Re: Hamiltonian

I agree with what Tamara said about the Hamiltonian representing the double derivative, so H$\Psi$ is the double derivative of the wave function. However, I'm pretty sure we have to think about the Hamiltonian as an operator, not a variable, so it represents a mathematical function being done to a value but does not have any value itself.

reyvalui_2g
Posts: 40
Joined: Wed Sep 30, 2020 9:52 pm

### Re: Hamiltonian

If I remember correctly, the Hamiltonian represents the kinetic energy of the wave function plus the potential energy of the wave function.

The kinetic energy of the wave function represents the energy of the actual motion of the particle, while the potential energy of the wave function represents the motion that the particle could have.