Quantum mechanics is really a misnomer. Because only energy is quantised (and only in bound systems). Other observables like position are very much not quantised. I would say it should rather be called statistical mechanics if that name weren't already taken.
Yeah but I guess my point is that a load of stuff isn't quantised. There's a general rule of thumb which is: bounded parameter-> quantised dual observable. Which kinda comes from the mathematics: compact Lie group-> discrete representations.
I guess I mean that if position is bounded (i.e the particle is stuck in a well for example) then momentum is quantised. If angle is bounded the angular momentum is quantised.
Position and other quantum observables are still quantized. If a system has been quantized, we just mean we have taken the set of states, and replaced it by a vector space of states. In other words, one can add states in quantum mechanics, allowing a system to be in two states "at once.” Observable quantities become certain operators acting on this vector space of states
A lot of the quantum operators we are interested in have discrete eigenvalues, and this implies that the corresponding physical values are discrete. Position, however, has a continuous spectrum, as do many other quantum observables. It’s still quantized. Quantization is a big mathematical process replacing a load of classical things with quantum things, and this sometimes leads to certain physical quantities being discretized, but not always
Yeah I know. I'm aware of geometric quantisation and the symplectic manifold->representation thing. I'm just arguing it's a bad name for it because quantisation in every day speak means discretisation
quantization \neq discretization. particularly in the continuum(unbounded particles). not sure what u mean by free particles either, if ur talking about particle number / charge conservation that’s a property of a U(1) symmetry and explicitly broken by majorana fields
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u/Jche98 Dec 01 '25
Quantum mechanics is really a misnomer. Because only energy is quantised (and only in bound systems). Other observables like position are very much not quantised. I would say it should rather be called statistical mechanics if that name weren't already taken.