Position-dependent mass (PDM) systems have diverse applications in physics, attracting significant scientific interest in the last decades. Classical PDM systems pose analytical challenges with their nonlinear equations of motion, while the quantum case is complicated because the kinetic operator is non-Hermitian. To address these challenges, this study explores Hamiltonian factorization and canonical transformations to investigate classical and quantum PDM systems, applying it to a Mathews-Lakshmanan-type oscillator with m ( x ) = 1 / [ 1 + ( λ x ) 2 ]. Classically, the phase space is examined, revealing increasingly pronounced deformities in the trajectories as energy and λ values increase. In the quantum realm, the solution to the ambiguous ordering problem for the PDM oscillator is presented, accompanied by an analysis of wave functions and probability densities. Further, the tunneling probabilities are analyzed. As λ increases, findings indicate that the tunneling probabilities of the PDM system decrease fast for higher excited states, offering novel insights into its behavior.

Nos últimos anos o emprego do titanato de bário (BaTiO3) na indústria de cerâmicas tecnológicas e em dispositivos optoeletrônicos tem se incrementado em decorrência de suas propriedades ferroelétricas, termoelétricas, piezoelétricas e ópticas. O objetivo deste trabalho foi sintetizar e caracterizar pós e filmes finos amorfos de titanato de bário (BaTiO3), por meio do método Pechini. Esses pós foram caracterizados via Análise Térmica (TG/DSC) e Difração de Raios X (DRX). A temperatura utilizada no tratamento térmico dos pós foi de 400°C a 800°C dependendo da amostra, durante 10 horas. A análise estrutural de DRX revelou um aumento da linha espectral, que pode ser observada em alguns difratogramas, próxima do ângulo de 30° em 2q, sugerindo uma maior cristalinidade e um aumento do tamanho do cristalito provocado pelo aumento da temperatura de calcinação. Essas análises indicaram também a presença de BaCO3, além disso, observou-se a formação de apenas um pico próximo a 45° em 2q, sugerindo a formação de titanato com fase cúbica. A partir dos difratogramas foi calculado o tamanho de grão, o resultado obtido foi da ordem de 20 nm. Os filmes finos de BaTiO3 foram depositados via Dip Coating. Esses filmes foram analisados por meio da Microscopia de Força Atômica (AFM). Esta técnica permitiu observar aglomerações de partículas em todos os filmes. A superfície desses filmes apresentou alterações significativas em sua rugosidade com aumento da temperatura de tratamento térmico dos filmes.

In recent years the use of barium titanate (BaTiO3) in ceramics industry technology and optoelectronic devices has increased due to their ferroelectric, thermoelectric, piezoelectric and optical properties. The objective of this study was to synthesize and characterize amorphous powders and thin films of barium titanate (BaTiO3), through the Pechini method. These powders were characterized via thermal analysis (TG / DSC) and X-Ray Diffraction (XRD). The temperature employed in the heat treatment of the powders was 400° C to 800° C depending on the sample, for 10 hours. Structural analysis of the XRD revealed an increase in the spectral line which can be observed in some diffractograms patterns near to the angle of 30º 2θ, suggesting a higher crystallinity and an increase in crystallite size caused by the increase of the calcination temperature. These tests also indicate the presence of BaCO3 and was also observed the formation of only one peak at 45° 2θ, suggesting the formation of cubic phase with titanate. Through the results obtained from the XRD the grain size was calculated, whose dimensions gotten were approximately 50 nm. BaTiO3 thin films were deposited by dip coating. These films were studied by atomic force microscopy (AFM). This technique allowed us to observe clusters of particles in every film. The surface of these films presented significant changes in roughness with increasing temperature heat treatment of films.