Schrodinger – Learn

Applying wave properties to electron orbits

The limitations of Bohr’s model of the atom have previously been descirbed. While it was able to explain the organisation of electrons around the nucleus, it was an incomplete model, unable to be applied to larger atoms or explain the stability of orbits. It took de Broglie’s proposal of matter waves and the subsequent experimental validation of his hypothesis by Davisson and Germer, to unlock the quantum nature of the electron orbits. 

Erwin Schrödinger was an Austrian physicist, who is most famous for his thought experimental involving a cat, a box, radioactive decay and some poison. However, while this sounds quite interesting, it does not really contribute to an understanding of electron orbitals. As with many other advances to the atomic model, Schrödinger built upon existing models and theories to create a more refined representation of the atom. Accepting the limitations of Bohr’s model, he considered the work of de Broglie, applying wave properties to the steady orbits of electrons.

In the findings of the Davisson and Germer experiment, the detected paths of the electrons indicated that they were exhibiting a wave property, interference. Led Schrödinger to suggest that standing wave patterns could be applied to the motion of electrons. This has became one of the pillars of quantum mechanics.

Standing waves

In Module 3, standing waves were introduced. Standing waves are formed when waves of the same frequency interact on the same plane. They can be easily modeled with a long spring, seeming to contain places where the wave does not move separated by areas of maximum movement, or displacement. The areas of no displacement are called nodes, and the areas of maximum displacement are named antinodes. The diagram below shows four standing waves, the top containing two nodes and one antinode and the last containing five nodes and four antinodes. 

As can be seen, standing waves are discrete and can have only contain a whole number amount of nodes and antinodes. For example, a standing wave cannot exist with with two and a half nodes, it will either have two or three. Standing waves have a prominent place in physics long being used to describe harmonics and were used by Heinrich Hertz to confirm the existence of electromagnetic radiation beyond visible spectrum, confirming one of Maxwell’s proposals.

Schrödinger applied standing waves to electron orbits, uniting Bohr’s model with the matter waves described by de Broglie. He suggested that the quantised orbits were related to specific standing waves patterns formed by the electrons, in doing so, explaining the specific energy states in an atom. Schrödinger’s model, as seen on the left below, demonstrates the application of standing waves to quantised orbitals. The image on the right showing the impact of incomplete standing waves, which would lead to the destructive interference and the collapse of the model. 


The wave equation

When examining Schrödinger’s contribution to to quantum mechanics, it is common to be directed to his wave equation. This is a very complex relationship, which requires a deep understanding of mathematics and probability. Utilising the wave equation, an expression can be found for the probability of finding an electron in an area surrounding a nucleus. Given the complexities of the equation itself, and the impacts of the Heisenberg uncertainty principle, it beyond the scope of this course.