ChemTalk

# Heisenberg’s Uncertainty Principle

## Core Concepts

In this article you will learn about one of the fundamental principles on quantum mechanics, the uncertainty principle. After reading the article you’ll fully understand the electron duality and the basis of the principle

## Topics Covered in Other Articles

The Uncertainty Principle, formulated by Werner Heisenberg, states that we can’t know the exact position and momentum/velocity of a particle at the same time with perfect accuracy; the more we know about the photon or electrons speed, the less we know about its position, and vice versa. This principle tells us about limits and behaviors inside quantum mechanics.

## Werner Heisenberg

Werner Karl Heisenberg was a German theoretical physicist, who focused his studies on quantum mechanics. He is best known for formulating the Uncertainty Principle, which was published in 1927, five years later he was awarded the Nobel Prize in physics for the “The creation of quantum mechanics, the use of which has led, among other things, to the discovery of allotropic forms of hydrogen.”.

He was born on December 5th, 1901 in Wüzburgo and studied at the Munich University. Heisenberg was Max Borns assistant in 1923. From 1924 to 1927 he got a scholarship to work with Niels Bohr at the Copenhagen University. Werner was the leader researcher on the atomic bomb project during World War II.

During his doctorare years, he met Wolfgang Pauli. Pauli recommended that he dedicate himself to studying atomic theory, instead of the theory of relativity, since there was a greater field of study. Heisenberg and Pauli collaborated together in quantum mechanics.

## The Electron on the Uncertainty Principle

An electron is a particle, but it also behaves like a wave. It has a mass (m)and a velocity (v). The natural duality of the electron is demonstrated by the de Brogile relation; h being plank’s constant.

You can’t see an electron as a particle and know its exact position, while you can’t know its precise velocity or momentum when it acts as a wave, at the same time. In short, you can see the electron as a particle or as a wave, but not both at the same time. Position and momentum are complementary properties of the electron.

Since its exact position cannot be known, the probability of where the electron can be found within the atom is used, this is called probability density. This density is shown by the Electron Cloud Model.

### Double Slit Experiment

The double-slit experiment is one of the most famous physics experiments. This experiment shows the dual nature of the electron and suggests that observing the particles may affect their behavior.
The experiment consists of a wall with two slits with a screen behind. If an observer or something is monitoring the path of the electron through the slits it will not create interference, meaning they will only pass through the slits. On the other side, if there is no observer, the electron will cause an interference pattern, meaning the electron would have passed through the two slits at the same time, acting as a wave.

## The Uncertainty Principle

During 1923 and 1925 Werner Heisenberg studied a way to study quantum systems. He wanted to study a different way to Schrödinger’s theory, that involved wave functions. This principle was based on Heisenbergs matrix studies.

Heisenberg’s Uncertainty Principle, first proposed by Heisenberg in 1927. The principle was then derived by Earle Kennard and Hermann Weyl in 1928. This is based on this reciprocal behavior between momentum (p), and position (x), as well as between energy (E), and time (t). We can find his equation in different forms:

xp ≥ h/4π // tE ≥ h/4π

When you get closer to knowing the position, the value of momentum becomes less accurate. Knowing the position of an electron at 1 nanometer moves the speed of the electron 58 kg/s away.

Summarizing, the Uncertainty Principle is a proposal on how much information in a quantum system is fundamentally reachable. It is a natural consequence of the description of particles as the superposition of waves, waves which may be described in terms of either position or velocity. The inability to know both concurrently with absolute accuracy is a characteristic of the wave function itself. The ambiguity in the other creates the precision in the first. An unlimited number of momentum particles, each of which occupies a position in the universe, make up a completely special localized particle.