What Is Quantum Mechanics Good for?
Max Born said that by manipulating this wave function that Schrödinger developed, you could tell the probability of finding the electron at any point in space and time. From that, it turns out that the electron can only have certain discrete energies inside an atom. This had been discovered experimentally; this is the source of the famous line spectrum that atoms exhibit and that accounts for why neon lights are red whereas sodium streetlights have a yellow tinge. It has to do with the line spectra of their respective elements.
But to have an actual understanding of where these discrete energies come from—that electrons and atoms can only have certain energies and no other—is one of the most amazing things about quantum mechanics. It’s as though you are driving a car on a racetrack and you are only allowed to go in multiples of 10 miles per hour. When you take that and you bring many atoms together, all of those energies broaden out into a band of possible energies.
I like the point about how in basic discovery, nobody is thinking about applications down the line — Schrödinger didn’t have the diode laser in mind when he was developing the theory
If you went to Schrödinger in 1926 and said, “Nice equation, Erwin. What’s it good for?” He’s not going to say, “Well, if you want to store music in a compact digital format…”