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

Mentor
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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.

Homework Helper
Gold Member
2022 Award
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.