# How the Schrödinger Equation Contributed to Quantum Mechanics

From the Lecture Series: Understanding the Misconceptions of Science

## When physicians began studying electrons and photons as both particles and waves, they found many confusing results. The Schrödinger equation helped them to detect where the electron could be at any given moment. The significance was that electrons had extremely unpredictable behaviors, but physicist Erwin Schrödinger’s experiment tamed the situation. Read on to see what he exactly did.

When scientists were studying light, they eventually found out that light acted like both a wave and a particle. They realized that electrons did the same, too. Previously, Niels Bohr explained the levels in an atom. When Louis de Broglie suggested that they might also be both wave and particle, things made more sense: there were discrete energy levels in atoms.

### The Schrödinger Equation

In 1925, Austrian physicist Erwin Schrödinger introduced an equation that contributed greatly to quantum mechanics. In simple terms, it describes what electrons do under almost any circumstances.

To do so, one needs to insert a term that describes the situation—the V. if an electron is somewhere that nothing happens, V is zero. If it gets close to an atom nucleus, V will have a different formula. The mathematical side is beyond the scope of this article, but the results fall right within the boundaries of our interest.

Initially, it shows how complex the atom orbitals are, with their varying shapes as either spheres or the shape of dumbbells.

This is a transcript from the video series Understanding the Misconceptions of Science. Watch it now, on Wondrium.

### Psi in the Schrödinger’s Equation

Psi, or the wave function, is the most important part of the Schrödinger equation: the answer. The solution to the Schrödinger equation is intended to describe the electron, and there can be an infinite number of solutions. However, the focus here is on psi, which equals the square root of Pi times e to the minus r, where r is related to the distance from the center of the atom.

For example, if the equation is used for a hydrogen atom, many things about it can be predicted: the radius of the atom and the wavelengths of light that hydrogen emits. What psi shows is actually the potential place where the electron could be.

### Where the Electron Is

Psi is biggest at the center of the atom, i.e., the nucleus. However, it does not necessarily mean that the electron is located at the center. This is because psi is not zero in many other places in the atom. At the same time, the electron can act like a wave, and this makes the situation more puzzling.

A German physicist called Max Born made things less puzzling in 1926 by explaining that the wave function was related to probability. In fact, when the psi function undergoes some mathematical operations, it can show the probability of the electron being where the new function says it is. This is how the Schrödinger equation can predict the place of the electron.

Even though psi has the highest amount at the center, there is zero probability that the electron is at the center. Another place with zero probability is very far away from the atom nucleus. Between the two zero-probability points, there is a radius where the probability is a maximum. However, that is not the only place where the electron could be.

### Classical Vs. Quantum Mechanics

Classical mechanics expects an electron to be like a planet orbiting the sun: at a specific radius, with a specific speed. The quantum realm not only explains why the classical view is wrong but also shows how the reality is.

Quantum mechanics here is built around probabilities. The wave function, or psi, is used to calculate these probabilities. However, the tricky point here is to successfully avoid interpreting the quantum realm with classical tools and expectations. Classical mechanics expects electrons to orbit the nucleus like planets orbit the sun, but orbitals in the atom are not like planet orbits. (Image: Dabarti CGI/Shutterstock)

The probabilities of quantum mechanics do not specify where an electron is. What they show is where it is likely to be found. It is a bit complicated but real. According to quantum mechanics, an electron is simultaneously everywhere that the wave function says it is.

### The Collapse of the Wave Function

In the experiment where one photon and one electron were shot at narrow slits, each acted like particles. However, when enough electrons or photons were considered, the pattern looked like a wave. In other words, the wave function specified the probability, but the observation was at a point.

The same thing happens inside an atom. The electron can simultaneously be everywhere that the wave function says it can be. However, it is actually only at the point where it is detected. This is when the wave function collapses.

This means that when the electron is finally detected, the wave function’s probabilities are no longer valid for places where the electron is not located. Yet, if the wave function was spread out before the detection and not after, then the wave function changes when the detection occurs. This is the base of the collapse.

Thus, the Schrödinger equation made the complex and confusing world of quantum physics a bit more predictable and understandable.

### Common Questions about Schrödinger Equation

Q: What does the Schrödinger equation show?

The Schrödinger equation describes what electrons do under pretty much any circumstance.

Q: What is Psi in Schrödinger equation?

Psi is the answer to the Schrödinger equation, and all of the other elements and efforts are involved to solve for psi.

Q: What does the Schrödinger equation show about atom orbitals?

The Schrödinger equation shows that orbitals are more complex than expected. There are orbitals that are in the shape of spheres and others that are in the shape of dumbbells.

Q: What happens when the wave function collapses?

The Schrödinger equation made predicting what the electron does possible. If the electron is simultaneously everywhere that the wave function says it can be, but it is only found where it is detected, then the wave function, supposedly, collapses.