Why do authors write mathematical expressions in their books?

mathematicsquantum mechanicssoft-question

I'm currently interested in and new to QM and I'm reading a book, that teaches QM in an easy way. But there are many mathematical expressions about various things, like the quantum state of a spin when an apparatus is rotated along the x-, y- or z-Axis.

I can think of what the purpose of these expressions might be, but I want to know it more clearly.

What's the purpose of writing these mathematical expressions and do I really have to know/understand every single detail of these expressions or just generally know what they are?

Thank you !

PS: I'm currently not studying physics, but I'm thinking of studying physics in the future. ^^

Best Answer

Mathematics has some very useful properties that make it superior to natural language in describing physical theories:

  1. It is precise: an English sentence can be ambiguous and can be interpreted in wrong ways. A mathematical statement, when every term is well defined, can mean only one thing.
  2. It is coincise: the author of your book could ramble on and on about how the wave function behaves, how it evolves in different cases etc.. or they could just write down the Schrodinger equation. The single equation contains every possible case of every possible wave function, with no ambiguity. Of course, the difficult part is to solve the equation.
  3. It can describe the world: which is a non trivial property. Many physical processes (maybe all of them?) can be described with a mathematical theory.

This makes mathematics an invaluable tool for the physicist, especially in the context of quantum mechanics, where our common intuition fails.