We discuss the relationship between exact solvability of the Schroedinger equation, due to a spatially dependent mass, and the ordering ambiguity. Some examples show that, even in this case, one can find exact solutions. Furthermore, it is demonstrated that operators with linear dependence on the momentum are nonambiguous. *

In the last few years a number of works reported the appearance of thick branes with internal structure, induced by the parameter which controls the interaction between two scalar fields coupled to gravity in (4,1) dimensions in warped space-time with one extra dimension. Here we show that one can implement the control over the brane thickness without needing to change the potential parameter. On the contrary, this is going to be done by means of the variation of a parameter associated to the domain wall degeneracy. We also report the existence of novel and qualitatively different solutions for a critical value of the degeneracy parameter, which could be called critical Bloch branes.

In this work we present some classes of models whose the corresponding two coupled first-order nonlinear equations can be put into a linear form, and consequently be solved completely. In these cases the so-called trial orbit method is completely unnecessary. We recall that some physically important models as, for instance, the problem of tiling a plane with a network of defects and polymer properties are in this class of models.Comment: 14 pages, 3 figure

We present a different class of quantum-mechanical potentials. These are midway between the exactly solvable potentials and the quasiexactly ones. Their fundamental feature is that one can find the entire s-wave spectrum of a given potential, provided that some of its parameters are conveniently fixed. This type of approach has been used extensively in the path-integral method of quantization [8]. In fact, the above procedure was also used in the Schrodinger picture to relate different power-law potentials [9], and also to relate spherically symmetric potentials at different space dimensions [10]. However, for transformations where f (u)=u, with a being real, b, V(u) will always produce a u term, which should be removed in order to get a driven harmonic oscillator potential in the new variable. This is the origin, for the cases here considered, of the very particular fixing of one of the potential parameters.At this point it is interesting to make some considerations about the boundary conditions after the transformation r = f (u

In this work we analyze the localization of fermions on degenerate and critical Bloch branes. This is done directly on physical coordinates, in constrast to some works that has been using conformal coordinates. We find the range of coupling constants of the interaction of fermions with the scalar fields that allow us to have normalizable fermion zero-mode localized on the brane on both, critical and degenerate Bloch branes. In the case of critical branes our results agree with those found in [Class. Quantum Grav. 27 (2010) 185001]. The results on fermion localization on degenerate Bloch branes are new. We also propose a coupling of fermions to the scalar fields which leads to localization of massless fermion on both sides of a double-brane.

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We start this work by revisiting the problem of the soldering of two chiral Schwinger models of opposite chiralities. We verify that, different from what one can conclude from the current literature, the usual sum of these models is, in fact, gauge invariant and corresponds to a composite model, where the component models are the vector and axial Schwinger models. As a consequence, we reinterpret this formalism as a kind of degree of freedom reduction mechanism. This result has led us to discover a second soldering possibility giving rise to the axial Schwinger model. This new result is seemingly rather general. We explore it here in the soldering of two Maxwell-Chern-Simons theories with different masses.