Abstract
Mermin's "shut up and calculate!" somehow summarizes the most widely accepted view on quantum mechanics. This conception has led to a rather constraining way to think and understand the quantum world. Nonetheless, a closer look at the principles and formal body of this theory shows that, beyond longstanding prejudices, there is still room enough for alternative tools. This is the case, for example, of Bohmian mechanics. As it is discussed here, there is nothing contradictory or wrong with this hydrodynamical representation, which enhances the dynamical role of the quantum phase to the detriment (to some extent) of the probability density. The possibility to describe the evolution of quantum systems in terms of trajectories or streamlines is just a direct consequence of the fact that Bohmian mechanics (quantum hydrodynamics) is just a way to recast quantum mechanics in the more general language of the theory of characteristics. Misconceptions concerning Bohmian mechanics typically come from the fact that many times it is taken out of context and considered as an alternative theory to quantum mechanics, which is not the case. On the contrary, an appropriate contextualization shows that Bohmian mechanics constitutes a serious and useful representation of quantum mechanics, at the same level as any other quantum picture, such as Schrödinger's, Heisenberg's, Dirac's, or Feynman's, for instance. To illustrate its versatility, two phenomena will be briefly considered, namely dissipation and light interference.
Highlights
In 2013 we have celebrated the 100th anniversary of Bohr’s atomic model [1, 2], which led to the development of quantum mechanics in the 1920s
The integration in time of Eq (7) generates a family of streamlines or paths along which the quantum fluid propagates, just as in the case of a classical fluid. As it can be inferred, the first equality goes beyond Bohmian mechanics and allows to define streamlines in any system characterized by a certain density and a vector that transports it through the corresponding configuration space, regardless whether such a density describes a quantum system or not
Hydrodynamic approaches in the literature1 As seen above, the hydrodynamic language of Bohmian mechanics enables a visualization of quantum systems in terms of streamlines that follow the flow of the probability density
Summary
In 2013 we have celebrated the 100th anniversary of Bohr’s atomic model [1, 2], which led to the development of quantum mechanics in the 1920s. Quantum systems are described by a probability amplitude or wave function, Ψ, which evolves according to the partial differential equation i
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