H = xp and the Riemann Zeros
H = xp and the Riemann Zeros
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H = xp 和黎曼零点
DOI：
10.1007/978-1-4615-4875-1_19
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发表时间：
1999
影响因子：
1.8
通讯作者：
J. Keating
中科院分区：
文献类型：
--
作者：
M. Berry;J. Keating
黎曼假设1，2指出ζ(S)的复零点位于临界线Re S=1/2上，即(1)的非虚解En都是实的。在这里，我们将提供一些证据，证明En是能级，即与经典哈密顿量(2)有关的厄米量子算符(‘Riemann算符’)的本征值，其中x是(一维)位置坐标，p是共轭动量。坦率地说，这是投机性的，因为仍然存在巨大的差距，而不仅仅是技术上的差距。
The Riemann hypothesis 1,2 states that the complex zeros of ζ(s) lie on the critical line Re s=1/2; that is, the nonimaginary solutions E n of (1) are all real. Here we will present some evidence that the E n are energy levels, that is eigenvalues of a hermitian quantum operator (the ‘Riemann operator’), associated with the classical hamiltonian (2) where x is the (one-dimensional) position coordinate and p the conjugate momentum. This is frankly speculative, because large gaps remain that are not merely technical.