𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The Schrödinger and Dirac Free Particle Equations without Quantum Mechanics

✍ Scribed by G.N. Ord

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
351 KB
Volume
250
Category
Article
ISSN
0003-4916

No coin nor oath required. For personal study only.

✦ Synopsis

Einstein's theory of Brownian Movement has provided a well accepted microscopic model of diffusion for many years. Until recently the relationship between this model and Quantum Mechanics has been completely formal. Brownian motion provides a microscopic model for diffusion, but quantum mechanics and diffusion are related by a formal analytic continuation, so the relationship between Brownian motion and Quantum Mechanics has been correspondingly vague. Some recent work has changed this picture somewhat and here we show that a random walk model of Brownian motion produces the diffusion equation or the telegraph equations as a descriptions of particle densities, while at the same time the correlations in the space-time geometry of these same Brownian particles obey the Schro dinger and Dirac equations respectively. This is of interest because the equations of Quantum Mechanics appear here naturally in a classical context without the problems of interpretation they have in the usual context.

📜 SIMILAR VOLUMES

On the equivalence of the Schrödinger an
On the equivalence of the Schrödinger and the quantum Liouville equations
✍ Peter A. Markowich; H. Neunzert 📂 Article 📅 1989 🏛 John Wiley and Sons 🌐 English ⚖ 483 KB

## Communicated by H. Neunzert We present a semigroup analysis of the quantum Liouville equation, which models the temporal evolution of the (quasi) distribution of an electron ensemble under the action of a scalar potential. By employing the density matrix formulation of quantum physics we prove

3,5-contracted Schrödinger equation: Det
3,5-contracted Schrödinger equation: Determining quantum energies and reduced density matrices without wave functions
✍ David A. Mazziotti 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 351 KB 👁 1 views

Through the 3,5-contracted Schrodinger equation 3,5-CSchE quantum ¨Ž . energies and 3-particle reduced density matrices 3-RDMs are determined directly without wave functions. Since the 3,5-CSchE involves the 5-RDM, its solution is indeterminate without N-representability conditions. However, the ind