Manzetti Sergio
Fjordforsk A/S, Bygdavegen 155, 6894, Vangsnes, Norway.
Uppsala University, BMC, Dept Mol. Cell Biol, Box 596, SE-75124, Uppsala, Sweden.
Sci Rep. 2018 Nov 8;8(1):16572. doi: 10.1038/s41598-018-34836-3.
Quantum mechanical models for particles are strictly dependent on the Schrödinger equation, where the solutions and the Hermitian polynomials form a mathematical foundation to derive expectation values for observables. As for all quantum systems, the solutions are derived in discrete energy levels, and yield probability density, the kinetic energy and average momentum. In this study however, an attenuation Hamiltonian is derived by the algebraic relation of the momentum and position operators, and the derived equation, where the attenuation of kinetic energy is the eigenvalue, is studied numerically. The numerical solutions suggest that the change in kinetic energy from one transition to the next proceeds in an undular fashion, and not in a definite manner. This suggests that any sub-atomic particle which experiences a transition from one level to the next, does so by both gaining and losing energy in an undular manner before reaching an equilibrium with a new and stabilized kinetic energy. The results show also that the phase of the change in kinetic energy between transitions differs between high and low momenta and that higher levels of momentum attenuate more smoothly than transitions between lower energy levels. The investigated attenuation operator may be important for future pinning and quasipinning approaches and play a role in future quantum information processing. Future research is required on the spectrum of the operator and on its potential analytical solutions.
粒子的量子力学模型严格依赖于薛定谔方程，其中解和厄米多项式构成了推导可观测量期望值的数学基础。对于所有量子系统而言，解是在离散能级中得出的，并产生概率密度、动能和平均动量。然而，在本研究中，通过动量和位置算符的代数关系推导出一个衰减哈密顿量，并对以动能衰减为特征值的导出方程进行了数值研究。数值解表明，从一个跃迁到下一个跃迁的动能变化以波动的方式进行，而不是以确定的方式。这表明，任何经历从一个能级跃迁到下一个能级的亚原子粒子，在达到具有新的稳定动能的平衡之前，都是通过以波动的方式既获得能量又损失能量来实现的。结果还表明，跃迁之间动能变化的相位在高动量和低动量之间有所不同，并且较高动量水平的衰减比较低能级之间的跃迁更平滑。所研究的衰减算符可能对未来的钉扎和准钉扎方法很重要，并在未来的量子信息处理中发挥作用。需要对该算符的谱及其潜在的解析解进行进一步研究。
