Derivation of the non-linear Schrödinger equation from stochastic optimal control
作者:
Akira Ohsumi,
期刊:
International Journal of Control
(Taylor Available online 1989)
卷期:
Volume 49,
issue 3
页码: 841-849
ISSN:0020-7179
年代: 1989
DOI:10.1080/00207178908559671
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
The quantum-mechanical formulation of a class of stochastic optimal control problems is investigated and two versions of non-linear Schrödinger equation are derived. First, a wave-function is introduced which connects the probability density function of a diffusion process with the minimum cost functional of the stochastic optimal control problem associated with the diffusion process. It is then demonstrated that this wave-function satisfies a kind of Schrödinger-Langevin equation in quantum physics. Finally, the probabilistic interpretation of the wave-function is discussed.
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