Remarks concerning the derivation and the expansion of the master equation

✍ Scribed by M. Razavy

• Publisher: Elsevier Science
• Year: 1976
• Tongue: English
• Weight: 449 KB
• Volume: 84
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(76)90107-2

✦ Synopsis

The present work consist of two parts: In the first part we apply the method of quasilinearization to the differential equation describing the time development of the quantum-mechanical probability density. In this way we derive the master equation without resorting to perturbation theory. In the second part of the paper, for a general form of the master equation which is an integro-differential equation, we test the accuracy of the Fokker-Planck approximation with the help of a solvable model. Then we study an alternative way of reducing the integro-differential equation to a partial differential equation. By expanding the transition probability W(q, q'), and the distribution function in terms of a complete set of functions, we show that for certain forms of W(q, q'), the master equation can be transformed exactly to partial differential equations of finite order.