Schrodinger's Wave Picture of Electrons

Erwin Schrödinger is credited with developing our current understanding of the atom, although the theory would be impossible without the work of Bohr, Einstein, de Broglie, Heisenberg and others. In fact the period between 1900 and 1950 may have been the most cooperative and most productive era in all of physics. We will, in this text, refer to Schrödinger’s ideas with the full knowledge that credit for everything discussed is to some extent shared. 

Schrödinger’s work was mathematical - he wrote an equation that described the wave-behavior of electrons in atoms. We need to understand that equation (a little bit) but we also need to understand the theoretical meaning of that equation. This page is about the theory.

Thinking about the world in waves 

Schrödinger’s work treats the electrons in an atom as waves. This was possible because de Broglie had shown that electrons could be thought of as waves. Thinking of electrons was useful because waves had been studied extensively at this point in history so we had a great deal of experience writing equations that described wave behavior. In addition, multiple electrons in an atom could be thought of waves that interacted rather than as particles that repelled each other. 

To help you imagine what it means that multiple electrons in an atom are waves that interact, it may help to think about sound.

Imagine a single violin player suspended (somehow) in the middle of a concert hall. 

Now imagine that she plays a single note and that you can see the sound (rather than just hear it). In my head, I see a pale green sphere of sound surrounding her. Close to her violin, the color (and sound) is more intense and it fades gradually out as you move further away.

Arguably, there is no actual edge to the sound. It just fades out until you can’t hear (or see) it anymore, but it’s possible that someone with better hearing (or sight) would find that “edge further away. Remember that the nucleus (in this case the violinist) is incredibly small - so small that at this scale it would be invisible. That leaves us with a picture of the electron that looks something like this:

This is the way you MUST think about electrons to understand Schrödinger’s theory. When Schrödinger draws an s orbital, it looks like a circle, but this is VERY different from the circle that Bohr drew. Bohr’s circle is a ring ON which the electron particle IS. Schrödinger’s circle is a region of space that is filled with the electron wave slowly fading to nothing and with no actual edge.

Now let's ponder an atom with multiple electrons.