摘要：首次给出纳米颗粒哈密顿量的明确表示。根据纳米颗粒的量子自旋特性,得到纳米颗粒质量随时间变化的规律。根据纳米颗粒哈密顿量的守恒条件,得到纳米颗粒的量子平动动量、纳米颗粒的量子转动动量、纳米颗粒所受的量子引力及纳米颗粒与纳米颗粒引力中心的量子距离随时间变化的规律。证明纳米颗粒的量子平动动量、纳米颗粒与纳米颗粒引力中心的量子距离、纳米颗粒的量子能量均与颗粒所处的量子状态有关。对于不同量子状态的纳米颗粒,上述物理量的取值不同。本文中创新一组满足对易关系互为共轭的复量子数算符,建立纳米颗粒的量子算符代数理论,得到纳米颗粒能量的量子化表示。

关键词： 纳米颗粒；量子引力；量子尺寸；圆锥对数螺线

Abstract: The exact expression of Hamiltonian for a nano-particle was proposed firstly. The principle that its mass varies with time was set up on the basis of the quantum spin character of the nano-particles. According to the conservative condition of the Hamiltonian of a nano-particle, the laws thatthe quantum translationalm omentum, the quantum rotational mom entum , the quantum gravitational force and the quantum distance betw een the nano-particles' gravitational center vary with time were obtained. It is shown that the quantum translation momentum, the quantum distance between the nano-particles' gravitational center and quantum energy of the nano-particles all relates to the quantum state of the nano-particles.T he above quantum physical quantities take various values for differentquantum states of the nano-particle. The conjugate complex quantum operators that meet the commutative relationship are proposed firstly, the quantum operator algebraic theory for the nano-particles is set up and the quantized expression of the nano-particle's energy is obtained. 

Keywords: nano-particle; quantum gravitation; quantum size; conic logarithmic helical line