## Archive of posts with tag “statistical mechanics”

### Regularizing the partition function of a hydrogen atom

The partition function of a hydrogen atom diverges (only considering bound states). However, we can regularize it to get finite answers. Different regularizations give the same result. They largely agree with the physical arguments for the case of the hydrogen atom at room or cold temperature, but this should be considered a mere coincidence. The results from regularized partition functions cannot generally be trusted.

- Categories: physics
- Tags: statistical mechanics, complex, regularization, long paper

### A measure-theoretic formulation of statistical ensembles (part 2)

For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms.

- Categories: physics
- Tags: mathematical physics, statistical mechanics, functional analysis, measure theory, probability, long paper

### A measure-theoretic formulation of statistical ensembles (part 1)

For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms.

- Categories: physics
- Tags: mathematical physics, statistical mechanics, functional analysis, measure theory, probability, long paper