## Parts of the Schrodinger Equation

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

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

sarahforman_Dis2I
Posts: 109
Joined: Sat Aug 17, 2019 12:18 am

### Parts of the Schrodinger Equation

Hi all! I understand that we will not need to calculate the equation itself, but I am still confused on how the equation works. I understand that the hamiltonian is the double derivative, but what is it the double derivative of? Can someone please explain the parts of this equation?

Brian_Ho_2B
Posts: 221
Joined: Fri Aug 09, 2019 12:16 am

### Re: Parts of the Schrodinger Equation

sarahforman_Dis4l wrote:Hi all! I understand that we will not need to calculate the equation itself, but I am still confused on how the equation works. I understand that the hamiltonian is the double derivative, but what is it the double derivative of? Can someone please explain the parts of this equation?

The hamiltonian is the double derivative of the wave function with respect to x, or position. I'd love to be able to explain the components of the equation but I believe it would be beyond the scope of even multivariable calculus. The main important things to know about the equation is that it utilizes the concepts of wave/particle duality of electrons, Heisenberg's Indeterminancy Principle, and the wave function in order to produce an equation that can be used to solve for equations that represent what electron orbitals look like in a 3D coordinate plane. It is also used to determine three of the quantum numbers: n (shell number), l (subshell number), and ml (identifies the particular orbital in the subshell). The one limitation that the equation has is that it doesn't tell us what ms is, which is the spin number of the electron. However, we can figure that out using Aufbau's principle, Pauli Exclusion principle, and especially Hund's rule.