## Hamiltonian

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

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

Kelly Cai 4D
Posts: 55
Joined: Sat Jul 20, 2019 12:17 am

### Hamiltonian

What is a hamiltonian and how does it relate to a wavefunction squared and the probability density of finding an electron in a certain region?

Lauren Haight 1E
Posts: 73
Joined: Wed Sep 18, 2019 12:15 am
Been upvoted: 1 time

### Re: Hamiltonian

The Hamiltonian is an operator that acts on the wave function. When we multiply the hamiltonian and the wave function, we get energy times the wave function. The wave function squared however, is the probability of electron density, or the probability of finding an electron at a certain location in an orbital. Both have something to do with finding information about an electron in a system. However, the Hamiltonian acts as an operator on the wave function in Schrodinger's equation, and wave function squared has to do with probability density.

Megan_1F
Posts: 49
Joined: Thu Jul 25, 2019 12:16 am

### Re: Hamiltonian

What exactly is an operator? In terms of a Hamiltonian?