𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the equivalence of the Schrödinger and the quantum Liouville equations

✍ Scribed by Peter A. Markowich; H. Neunzert

Publisher
John Wiley and Sons
Year
1989
Tongue
English
Weight
483 KB
Volume
11
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

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 that the quantum Liouville operator generates a unitary group on L2 if the corresponding Hamiltonian is essentially self-adjoint. Also, we analyse the existence and non-negativity of the particle density and prove that the solutions of the quantum Liouville equation converge to weak solutions of the classical Liouville equation as the Planck constant tends to zero (assuming that the potential is sufficiently smooth).

📜 SIMILAR VOLUMES

The Schrödinger and Dirac Free Particle
The Schrödinger and Dirac Free Particle Equations without Quantum Mechanics
✍ G.N. Ord 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 351 KB

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 an

The recursive solution of the Schrödinge
The recursive solution of the Schrödinger equation
✍ Roger Haydock 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 644 KB

A new approach to the computational solution of the Schfbdinger equation is based on the partial transformation of the Hamiltonian to a tridiagonal matrix. The method is especially suited to tight-binding Hamiltonians encountered in solid state physics and permits of the order of iodegrees of freedo

On the resonance spectrum of the one-dim
On the resonance spectrum of the one-dimensional schrödinger equation
✍ O. Atabek; R. Lefebvre 📂 Article 📅 1981 🏛 Elsevier Science 🌐 English ⚖ 330 KB

The fmlte difference boundary value method wth a complex rotated coordmate IS used to obtain the resonances of the onednnensonal Schrodinger equation An example IS wnsldered which ylclds resonances wdh widths exceed= the real part of the enera