# Explain the Schrodinger equation

• Huzaifa
In summary, the Schrodinger wave equation in the quantum mechanics model of an atom is a mathematical tool that describes the behavior of particles on a quantum level. It involves the Laplace operator, which is a mathematical operator that measures the curvature of a function, and the Hamiltonian operator, which represents the total energy of the system. The wave function represents the probability of finding a particle at a certain position and time. However, understanding the Schrodinger wave equation requires knowledge of differential equations and basic calculus.

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

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

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

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.

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.

## 1. What is the Schrodinger equation?

The Schrodinger equation is a mathematical formula that describes the behavior of quantum particles, such as electrons, in a given system. It was developed by Austrian physicist Erwin Schrodinger in 1926 and is a fundamental equation in quantum mechanics.

## 2. How does the Schrodinger equation work?

The Schrodinger equation uses complex numbers and operators to describe the probability of finding a quantum particle in a certain location at a given time. It takes into account the particle's wave-like nature and the potential energy of the system.

## 3. What does the Schrodinger equation predict?

The Schrodinger equation predicts the probability of a quantum particle's position and momentum at a given time. It also predicts the energy levels of a particle in a potential well and the behavior of particles in a quantum system.

## 4. How is the Schrodinger equation used in real-world applications?

The Schrodinger equation is used in various fields, such as chemistry, physics, and engineering, to understand and predict the behavior of quantum systems. It is used to study the properties of atoms, molecules, and materials, and to develop technologies such as transistors and lasers.

## 5. Is the Schrodinger equation the only equation used in quantum mechanics?

No, the Schrodinger equation is one of several equations used in quantum mechanics. Other important equations include the Heisenberg uncertainty principle and the Dirac equation. These equations work together to describe the behavior of quantum particles and systems.