## Expansion of Shrodinger Equation [ENDORSED]

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

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

Michelle_Li_1H
Posts: 32
Joined: Wed Sep 21, 2016 3:00 pm

### Expansion of Shrodinger Equation

Hi,

I was reading through Chapter 1 and saw that the book included an expanded version of the Schrodinger equation ( $\large -\frac{hbar^2}{2m}* \frac{d^2\Psi }{dx^2} + V(x)\Psi = E\Psi$ ). I was wondering what this meant and if we needed to know it for quizzes or exams?

Thanks!

Chem_Mod
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### Re: Expansion of Shrodinger Equation  [ENDORSED]

The entire part in the parenthesis is just the Hamiltonian. You do not need to worry about solving it or anything, just know that it is the Hamiltonian which, when acted upon a wavefunction, returns the energy of the wavefunction. The same equation is usually simplified to the following:

$H\varphi=E\varphi$

Megan M 1L
Posts: 10
Joined: Wed Sep 21, 2016 2:59 pm

### Re: Expansion of Shrodinger Equation

What is meaning of the Hamiltonian? I mean, how does it relate in Schrodinger's equation? Is it just the change in the wave function?

Mia Navarro 1D
Posts: 52
Joined: Fri Sep 29, 2017 7:04 am

### Re: Expansion of Shrodinger Equation

The Hamiltonian is the energy that is enacted upon a wavefunction that changes gradually.