### Loosely-threaded thoughts [mostly] about mathematics and physics.

12 post articles, 2 pages.

## Multiparticle spaces in quantum mechanics, part 1: Indistinguishability

How do we represent states with multiple particles? It is not trivial to construct Hilbert spaces from scratch that represent indistinguishable particles, so what we do is construct a space that represents distinguishable particles, and then force that permutation of particle 'tags' is a symmetry.

## Mini-post: The periodic 1D wave equation

Wherein I very briefly discuss the general solution to the periodic 1D wave equation.

## Why is momentum the generator of translations?

In quantum mechanics, it is often stated that the momentum [operator] is the generator of translations. However, most texts fail to give a satisfactory justification to this claim, if any is given at all. What we will do here is define precisely what it means for observable to be a generator of a group of transformations, both in quantum and cla...

## A few words on mixed and pure states

I see that there is a bit of confusion between mixed and pure states in quantum mechanics. This is because the measurement of arbitrary observables for pure states is probabilistic, and this is easily confused with the probabilitites associated to a mixed state.