Abstract
The dependence of the ground-state energy E of a quantum-mechanical system on the parameter λ 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 m1+m2+m3− and m1+m2+m4− three- and four-particle mesic atoms and molecules featuring particles of various mass are presented.
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