The purpose of this work is to reconsider and critically discuss the conceptual foundations of modern biology and bio-sciences in general, and provide an epistemological guideline to help framing the teaching of these disciplines and enhancing the quality of their presentation in High School, Master and Ph.D. courses. After discussing the…

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

The behaviour of a quantum rod, pivoted at its lower end on an impenetrable floor and restricted to moving in the vertical plane under the gravitational potential, is studied analytically under the approximation that the rod is initially localized to a "small-enough" neighbourhood around the point of classical unstable equilibrium. It is shown…

Many modern theories which try to unify gravity with the Standard Model of particle physics, such as e.g. string theory, propose two key modifications to the commonly known physical theories: the existence of additional space dimensions; the existence of a minimal length distance or maximal resolution. While extra dimensions have received a wide…

We illustrate some of the techniques to identify chaos signatures at the quantum level using as guiding examples some systems where a particle is constrained to move on a radial symmetric, but non-planar, surface. In particular, two systems are studied: the case of a cone with an arbitrary contour or "dunce hat billiard" and the rectangular…

The spin of a top can be regarded as a fast variable, coupled to the motion of the axis which is slow. In pure precession, the rotation of the axis round a cone (without nutation), can be considered as the result of a reaction from the fast spin. The resulting restriction of the total state space of the top is an illustrative example, at…

The parametric oscillations of an oscillator driven electromagnetically are presented. The oscillator is a conductive pipe hung from a spring, and driven by the oscillating magnetic field of a surrounding coil in the presence of a static magnetic field. It is an interesting case of parametric oscillations since the pipe is neither a magnet nor a…

The generalized second-order partial derivatives of 1/r, where r is the radial distance in three dimensions (3D), are obtained using a result of the potential theory of classical analysis. Some non-spherical-regularization alternatives to the standard spherical-regularization expression for the derivatives are derived. The utility of a…

By using the symmetry and time-independence properties of Schwarzschild spacetime it is demonstrated that an energy conservation law may be expressed in terms of local velocity. From this form three important results may be derived very concisely. This highlights analogies and differences between relativistic and classical approaches to mechanics…

The requirement of rotational invariance for lattice potential energies is investigated. Starting from this condition, it is shown that the Cauchy relations for the elastic constants are fulfilled if the lattice potential is built from pair interactions or when the first-neighbour approximation is adopted. This is seldom recognized in widely used…

A core topic in graduate courses in electrodynamics is the description of radiation from an accelerated charge and the associated radiation reaction. However, contemporary papers still express a diversity of views on the question of whether or not a uniformly accelerating charge radiates suggesting that a complete "physical" understanding of the…

In a recent paper (Denny 2002 Eur. J. Phys. 23 449-58), entitled "The pendulum clock: a venerable dynamical system", Denny showed that in a first approximation the steady-state motion of a weight-driven pendulum clock is shown to be a stable limit cycle. He placed the problem in a historical context and obtained an approximate solution using the…

Theories of wetting of liquids on solid surfaces under the condition that van der Waals force is dominant are briefly reviewed. We show theoretically that Zisman's empirical equation for wetting of liquids on solid surfaces is a linear approximation of the Young-van der Waals equation in the wetting region, and we express the two parameters in…

It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical…

In continuation of a previous work, we present an analytic study of ascending vertical motion of a rocket subjected to a quadratic drag for the case where the mass-variation law is a linear function of time. We discuss the detailed analytical solution of the model differential equations in closed form. Examples of application are presented and…