Cycling in Quantum and Classical Statistical Mechanics
| Main Author: | Francesco R. Ruggeri |
|---|---|
| Format: | info publication-preprint |
| Terbitan: |
, 2018
|
| Subjects: | |
| Online Access: |
https://zenodo.org/record/1563500 |
Daftar Isi:
- A bound quantum state wavefunction has a factor exp(iEt), where E is the energy, but in the calculation of the density, which is a physical observable, it disappears. In this note, as in some previous notes, we argue that exp(iEt) which represents cycling is a driving factor of a quantum mechanical description. It allows for physical dynamics in the wavefunction which are not visible in the overall density. This physical dynamics at the wavefunction level seems to be linked to P(p\x), the probability of having a momentum p at a given x (i.e. p depends on x) and the idea of flow based on average energy conservation at each point. In this note, we would particularly like to focus on extending this idea to the classical statistical mechanical harmonic oscillator. In statistical mechanics, one considers a constant T temperature with a Maxwell-Boltzmann velocity distribution throughout space and a changing spatial density to create force balance if there is a potential. In such a picture, it seems that there are no dynamics. We try to argue that the quantum mechanical ground state picture of an oscillator may actually have physical relevance to the classical statistical oscillator and that dynamics, even in classical statistical mechanics, may be brought in through a wavefunction type object which is relate to P(p\x) i.e. p depending on x. In a previous note, we tried to link the classical statistical oscillator to quantum mechanics by showing that in for such a potential the term W(x)V(x)W(x), where W(x) is the wavefunction, can be written as Shannon’s entropy. Here we wish to use only cycling arguments.