Imprints of the Quantum World in Classical Mechanics

被引：0
作者：
Maurice A. de Gosson
Basil J. Hiley
机构：
[1] Universität Wien,NuHAG, Fakultät für Mathematik
[2] University of London,TPRU, Birkbeck
来源：
Foundations of Physics | 2011年 / 41卷
关键词：
Quantization; Schrödinger’s equation; Hamiltonian flows; Symplectic covariance of Weyl calculus; Stone’s theorem;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show that the Schrödinger equation for a nonrelativistic spinless particle is a classical equation which is equivalent to Hamilton’s equations. Our discussion is quite general, and incorporates time-dependent systems. This gives us the opportunity of discussing the group of Hamiltonian canonical transformations which is a non-linear variant of the usual symplectic group.
引用
收藏
页码：1415 / 1436
页数：21
相关论文
共 21 条
[1]  
Banyaga A.(1978)Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique Comment. Math. Helv. 53 174-227
[2]  
Derbes D.(1996)Feynman’s derivation of the Schrödinger equation Am. J. Math. Phys. 64 881-884
[3]  
Feynman R.P.(1948)Space-time approach to non-relativistic quantum mechanics Rev. Mod. Phys. 20 367-387
[4]  
de Gosson M.(2009)The symplectic camel and the uncertainty principle: the tip of an iceberg Found. Phys. 99 194-214
[5]  
de Gosson M.(2009)Symplectic capacities and the geometry of uncertainty: the irruption of symplectic topology in classical and quantum mechanics Phys. Rep. 484 131-179
[6]  
Luef F.(1985)Pseudoholomorphic curves in symplectic manifolds Invent. Math. 82 307-347
[7]  
Gromov M.(2002)Schrödinger equation from an exact uncertainty principle J. Phys. A, Math. Gen. 35 3289-48
[8]  
Hall M.J.W.(1965)The Commun. Math. Phys. 1 114-291
[9]  
Reginatto M.(1986)-algebras of a free boson field Phys. Rep. 138 193-48
[10]  
Kastler D.(1966)The semiclassical evolution of wave packets Commun. Math. Phys. 2 31-58
123