How can one probe Podolsky Electrodynamics?

We investigate the possibility of detecting the Podolsky generalized electrodynamics constant $a$. First we analyze an ion interferometry apparatus proposed by B. Neyenhuis, et al (Phys. Rev. Lett. 99, (2007) 200401) who looked for deviations from Coulomb's inverse-square law in the context of Proca model. Our results show that this experiment has not enough precision for measurements of $a$. In order to set up bounds for $a$ we investigate the influence of Podolsky's electrostatic potential on the ground state of the Hydrogen atom. The value of the ground state energy of the Hydrogen atom requires Podolsky's constant to be smaller than 5.6 fm, or in energy scales larger than 35.51 MeV.Comment: 12 pages, 2 figure

Quantum mechanical virial theorem in systems with translational and rotational symmetry

Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If the conditions of translational and rotational symmetry together with the additional conditions of the theorem are satisfied, the matrix elements of the commutator [G, H] are equal to zero on the subspace of the Hilbert space. Normalized simultaneous eigenvectors of the particular set of commuting operators which contains H, J^{2}, J_{z} and additional operators form an orthonormal basis in this subspace. It is expected that the theorem is relevant for a large number of quantum mechanical N-particle systems with translational and rotational symmetry.Comment: 24 pages, accepted for publication in International Journal of Theoretical Physic