Quantum mechanics resumed

Karl De Paepe

Some paradoxes in quantum mechanics arising from coordinate transformations are presented. Resume Ce travail presente quelques paradoxes survenant en mecanique quantique apres transformations de coordonnees.

L. L. J. Vick

G. Feild

Hiroshi Tsukahara, Takeo Inami

We investigate the analyticity property of the partially resummed series expansion(PRSE) of the partition function for the eight-vertex model. Developing a graphical technique, we have obtained a first few terms of the PRSE and found that these terms have a pole only at one point in the complex plane of the coupling constant. This result supports the conjecture proposed by Guttmann and Enting concerning the “solvability ” in statistical mechanical lattice models. Recently Guttmann and Enting introduced a new point of view into the study of the solvability of lattice models in the statistical mechanics, including models for combinatorial problems [1]. Their approach is based on a study of the connection between the solvability of lattice models by use of the inversion relation and the analyticity properties of their associated series expansion, which is called the partially resummed series expansion(PRSE). For exactly solvable models, the inversion relation for the partition function was derived using the star-triangle relation [2,3]. Subsequently, it was shown to hold true for the partition

Peter Oto Hess

The hydrogen atom is investigated, within a pseudo-complex extension of the coordinates and momenta, which introduces a minimal length scale (l) and results into a non-commutative Quantum Mechanics. After resuming the pseudo-complex extension of Quantum Mechanics, the modified energies of the hydrogen atom are deduced, producing corrections of the order of the square of the minimal length scale. Using the Lamb Shift, we obtain an upper boundary for the minimal length scale l, orders of magnitude more restrictive than former estimations.