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Convexity Relation for Energy in Quantum Mechanics

机译:量子力学中能量的凸关系

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摘要

The dependence of the ground-state energy E of a quantum-mechanical system on the parameter lambda appearing linearly in the Hamiltonian is studied. A variation of the scale makes it possible to supplement the convexity-concavity relation for energy as a function of this parameter with a refined relation between the energies of systems that go over to one another upon a change in the particle charges or masses. This relation follows from the fundamentals of quantum mechanics and is valid for exact energies of the systems being considered. Its application does not require calculating wave functions and makes it possible to determine the boundaries of the ground-state energy level and the boundaries of the region of obvious stability of various systems. The results of applying the theory to m(1)(+)m(2)(+)m(3)(-) and m(1)(+)m(2)(+)m(3)(-)m(4)(-) three- and four-particle mesic atoms and molecules featuring particles of various mass are presented.
机译:研究了量子力学系统的基态能量E与哈密顿量线性出现的参数lambda的相关性。尺度的变化使得有可能根据该参数利用能量的凸凹关系来补充具有随着粒子电荷或质量的变化而彼此重叠的系统的能量之间的精细关系。这种关系遵循量子力学的基础,对于所考虑的系统的确切能量是有效的。它的应用不需要计算波函数,并且可以确定基态能级的边界和各种系统的明显稳定性区域的边界。将理论应用于m(1)(+)m(2)(+)m(3)(-)和m(1)(+)m(2)(+)m(3)(-)的结果提出了m(4)(-)三粒子和四粒子中观原子以及具有各种质量粒子的分子。

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