Exact quantum states of a general time-dependent quadratic system from classical action

A generalization of driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization which gives a general quadratic Hamiltonian system does not change the classical equation of motion. Based on the observation by Feynman and Hibbs, the propagators (kernels) of the systems are calculated from the classical action, in terms of solutions of the classical equation of motion: two homogeneous and one particular solutions. The kernels are then used to find wave functions which satisfy the Schr\"{o}dinger equation. One of the wave functions is shown to be that of a Gaussian pure state. In every case considered, we prove that the kernel does not depend on the way of choosing the classical solutions, while the wave functions depend on the choice. The generalization which gives a rather complicated quadratic Hamiltonian is simply interpreted as acting an unitary transformation to the driven harmonic oscillator system in the Hamiltonian formulation.Comment: Submitted to Phys. Rev.

Depression and quality of life in Brazilian and Portuguese older people communities

We aimed to compare the association of depression with aspects of quality of life (QoL) among older people users of primary health care (PHC) living in Brazil and Portugal. We carried out an observational, cross-sectional and comparative study with a quantitative approach in the PHC scope in Brazil and Portugal, where we obtained a nonrandom sample of 150 participants aged 65 years or older (100 Brazilians and 50 Portuguese). We used the socioeconomic and health data questionnaire, the Medical Outcomes Short-Form Health Survey QoL (SF-36) questionnaire and the Beck Inventory. Among the socioeconomic profiles, most were females aged between 65 and 80 years in both countries. There was a significant difference between groups in the income variable, with 100.0% of Portuguese people earning up to 1 minimum wage (P value 50.0) within the categorical variables of “absent” and “mild” depression. The Emotional role functioning, Physical role functioning, Physical functioning, Mental health, Total score domains and the Mental health and Physical health summary measures stood out with this behavior in Brazil and in Portugal, where these latter 2 presented moderate to strong correlation values (ρ > 0.400) in Portugal. Greater associations of depression on QoL were revealed in Portugal than in Brazil. Among their most expressive associations, the Physical role functioning (odds ratio [OR] = 4.776; 95.0% confidence interval [CI]: 2.41–9.43), Physical functioning (OR = 3.037; 95.0% CI: 3.037), Vitality (OR = 6.000; 95.0% CI: 1.56–23.07) and Total score (OR = 3.727; 95.0% CI: 2.24–6.17) domains and the Mental health summary measure (OR = 3.870; 95.0% CI: 2.13–7.02) stood out. Aspects related to the emotional, physical, functional and mental health components stood out. The association and correlation with depression were more expressive in Portugal compared to Brazil. However, similar results were obtained in Brazil but with less relevance