Flux/Flow and Probabilistic Considerations
| Main Author: | Francesco R. Ruggeri |
|---|---|
| Format: | info publication-preprint Journal |
| Terbitan: |
, 2022
|
| Subjects: | |
| Online Access: |
https://zenodo.org/record/6039392 |
Daftar Isi:
- In previous notes (1) we discussed two flux/flow equations dA(x,t)/dx partial = p and dA/dt partial=-E with a solution A(x,t)=-Et+px which is the relativistic free particle Lagrangian -mosqrt(1-vv) (c=1). We argued that one may convert these into two probabilistic eigenvalue equations representing free particle (relativistic or nonrelativistic) quantum mechanics: -id/dx partial exp(iA) = pexp(iA) and id/dt partial exp(iA) = E exp(iA). In this note we try to explore the relationship to probability more closely. In particular, we try to show that for a quantum bound state the main statistical principle is not maximization of entropy, but rather local conservation of energy i.e. a constant En at each x which is a consequence of special relativity (even in the nonrelativistic case). In other words an En (average energy) must be defined in order that a 4-vector (0,En) have meaning at each x.