## Shrodinger Equation;

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

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

josephyim1L
Posts: 61
Joined: Fri Sep 28, 2018 12:15 am

### Shrodinger Equation;

Can someone explain the primary significance of H(psi) = E(psi) and its relationship to finding the density probability of an electron. How this equation relates to the orbitals explained in class was very confusing.

skyeblee2F
Posts: 62
Joined: Fri Sep 28, 2018 12:23 am

### Re: Shrodinger Equation;

Basically...

The Schrodinger Equation is used to understand the physical properties of a system. The wave function (psi) exists in three dimensions (x,y,z), so solving for psi yields three quantum numbers. These three numbers define the energy shell occupied by the electron, energy subshell, and orientation of the subshell.

The square of psi determines the actual shape of orbitals and these shapes are referred to as probability densities. The shape is like a 3d map of space around the nucleus that shows where an electron is highly likely to be.

In the wave function, the values where a solution exists (or where an electron is likely to be) are limited to certain energy values (E, also called energy eigenvalues). In order to find the E of a wave-particle, you would apply the Hamiltonian operation (H) to the wave function. The nature of the Hamiltonian operator as a double derivative essentially "pulls out" the E from the wave function.

I do not think you have to know much about the mathematics behind the wave function itself, just what it represents conceptually.