一维最接近量子谐振子：Riemann函数的素数和零点的Hilbert-Polya哈密顿量
The One Dimensional Approachissimo Quantum Harmonic Oscillator: The Hilbert-Polya Hamiltonian for the Primes and the Zeros of the Riemann Function
摘要：
我已经对一维量子振荡器做了充分的研究，范围从对数势到指数势。我发现，具有极限（接近最小）谐振势（~ p（x）2）的谐振子的哈密顿量的本征值将黎曼函数高度的零点映射到黎曼线上。这是由J（x）的场产生的势，J（x）是素数计数函数p（x）的黎曼生成元，而p（x）又可以通过黎曼zeta函数的积分变换来定义。这起着量子限幅谐振子的弹簧强度的作用。这个结果的数论意义是zeta函数的根的高度是哈密顿量的特征值，其势是素数的平方到给定x的数量。因此这可能证明从未发表过的希尔伯特-波利亚猜想。该猜想是正确的，但并不意味着黎曼假设的真理。我们可以有复共轭零点的黎曼线和映射到另一个厄米算子，并给出了一般表达式。线外零点影响特征值的波动，但不影响其均值。
英文摘要：
I have made an ample study of one dimensional quantum oscillators, ranging from logarithmic to exponential potentials. I have found that the eigenvalues of the hamiltonian of the oscillator with the limiting (approachissimo) harmonic potential (~ p(x)2) maps the zeros of the Riemann function height up in the Riemann line. This is the potential created by the field of J(x) that is the Riemann generator of the prime number counting function, p(x), that in turn can be defined by an integral transformation of the Riemann zeta function. This plays the role of the spring strength of the quantum limiting harmonic oscillator. The number theory meaning of this result is that the roots height up of the zeta function are the eigenvalues of a Hamiltonian whose potential is the number of primes squared up to a given x. Therefore this may prove the never published Hilbert-Polya conjecture. The conjecture is true but does not imply the truth of the Riemann hypothesis. We can have complex conjugated zeros off the Riemman line and map them with another hermitic operator and a general expression is given for that. The zeros off the line affect the fluctuation of the eigenvalues but not their mean values.
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