Explain the Schrodinger equation

[Huzaifa]

Homework Statement

Please explain in simple words, the meaning of the Schrodinger wave equation in the quantum mechanics model of atom.

Relevant Equations

$$\frac{\partial^{2} \psi}{\partial x^{2}}+\frac{\partial^{2} \psi}{\partial y^{2}}+\frac{\partial^{2} \psi}{\partial z^{2}}+\frac{8 \pi^{2} m}{h^{2}}(E-U) \psi=0$$

Please explain in simple words, the meaning of the Schrodinger wave equation in the quantum mechanics model of atom. $$\frac{\partial^{2} \psi}{\partial x^{2}}+\frac{\partial^{2} \psi}{\partial y^{2}}+\frac{\partial^{2} \psi}{\partial z^{2}}+\frac{8 \pi^{2} m}{h^{2}}(E-U) \psi=0$$

 

[berkeman]

Welcome to PF.

We require that you show some effort on your schoolwork questions before we can offer tutorial help. What reading have you been doing about SE? What have you learned so far? What class is this for?

https://en.wikipedia.org/wiki/Schrödinger_equation

 

[Huzaifa]

$$
\nabla ^{2}\psi +\frac{8 \pi^{2} m}{h^{2}}(E-U) \psi=0
$$
$$
\frac{\partial^{2} \psi}{\partial x^{2}}+\frac{\partial^{2} \psi}{\partial y^{2}}+\frac{\partial^{2} \psi}{\partial z^{2}}+\frac{8 \pi^{2} m}{h^{2}}(E-U) \psi=0
$$

I am not able to understand the Laplace operator and the wave function. I do not have the knowledge of
differential equations. In the time-independent Schrödinger equation for Hydrogen atom, HΨ = EΨ, where H is Hamiltonian operator.

Please explain Laplace operator Hamiltonian operator and wave function without differential equations. Thank you.

 

[Steve4Physics]

You haven't answered the questions asked of you by @berkeman in Post#2 yet! And you haven't told us what you do understand - for example if you are familiar with basic calculus.