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We characterize point transformations in quantum mechanics from the mathematical viewpoint. To conclude that the canonical variables given by each point transformation in quantum mechanics correctly describe the extended point transformation, we show that they are all selfadjoint operators in $L^2(mathbb{R}^n)$ and that the continuous spectrum of each coincides with $mathbb{R}$. They are also shown to satisfy the canonical commutation relations.
We give a mathematically rigorous derivation of Ehrenfests equations for the evolution of position and momentum expectation values, under general and natural assumptions which include atomic and molecular Hamiltonians with Coulomb interactions.
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the study of sepa
Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has been used to
A new characterization of the singular packing subspaces of general bounded self-adjoint operators is presented, which is used to show that the set of operators whose spectral measures have upper packing dimension equal to one is a $G_delta$ (in suit
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the polarization bundle.