Abstract

The standard formulation of quantum mechanics, through Bohr’s complementarity principle and Heisenberg’s uncertainty between position and momentum conjugate variables, suggests that trajectories cannot be ascribed to quantum particles. Surprisingly, in 2011 A. M. Steinberg and co-workers [1] reported the observation of average trajectories of single-photons in a Young type double-slit experiment which reproduced those predicted by the de Broglie-Bohm formulation of quantum mechanics [2]. De Broglie-Bohm quantum mechanics provides an explanation of quantum phenomena in terms of point particles guided by wave functions. Although the de Broglie-Bohm and standard quantum theories have different formalisms, both yield exactly the same predictions for all quantum phenomena. In this talk, I will first review the de Broglie-Bohm formulation of quantum mechanics for a single non-relativistic quantum particle to later on show that this formulation is equivalent to that of ray optics beyond the eikonal approximation [3]. Thus, the quantum potential emerging in the de Broglie-Bohm formulation of quantum mechanics relates to a wave potential in the ray optics case. Then, I will discuss two examples on the use of the de Broglie-Bohm formulation to solve practical problems in quantum mechanics: (i) quantum transport of a single cold atom in a triple well potential [4]; and (ii) photoionization of a hydrogen atom with light beams carrying orbital angular momentum [5].

[1] “Observing the average trajectories of single photons in a two-slit interferometer”, S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, A. M. Steinberg, Science 332, 1170 (2011)

[2] “Applied Bohmian mechanics: from nanoscale systems to cosmology”, Eds. X. Oriols and J. Mompart, Pan Stanford Publishing, Singapore (2012).

[3] “Complete Hamiltonian description of wave-like features in classical and quantum physics”, A. Orefice, R. Giovanelli, D. Ditto, Found. Phys. 39, 256 (2009)

[4] “Need for relativistic corrections in the analysis of spatial adiabatic passage of matter waves”, A. Benseny, J. Bagudà, X. Oriols, J. Mompart, Phys. Rev. A 85, 053619 (2012)

[5] “Transferring orbital and spin angular momenta of light to atoms”, A. Picón, A. Benseny, J. Mompart, J.R. Vázquez de Aldana, L. Plaja, G.F. Calvo, L. Roso, New J. Phys. 12, 083053 (2010)