Consistency and Linearity in Quantum Theory
量子物理
2009-10-31 v1 统计力学
广义相对论与量子宇宙学
数学物理
math.MP
摘要
Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two answers must agree. The constraint is expressed in the form of functional equations the solution of which leads to the usual sum and product rules for amplitudes. An immediate consequence is that the Schrodinger equation must be linear: non-linear variants of quantum mechanics violate the requirement of consistency. PACS: 03.65.Bz, 03.65.Ca.
引用
@article{arxiv.quant-ph/9803086,
title = {Consistency and Linearity in Quantum Theory},
author = {Ariel Caticha},
journal= {arXiv preprint arXiv:quant-ph/9803086},
year = {2009}
}