What is quantum?
Let's start with the first big question: what is quantum mechanics, and what does the word "quantum" mean? This is a very good question and is almost always ignored in the study of quantum mechanics.
The word quantum comes from the word quantity. It generally refers to a discrete amount of something. In classical mechanics, we usually assume that quantities like energy or momentum can take any value from the real numbers.
\[ E, L, \dots \in \mathbb{R}. \]This is usually true in classical mechanics. However, in quantum physics, this is one of the many quantities that cannot always take a continuous set of values. Most of the time, quantities like energy comes in discrete quantities or discrete "quanta".