In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin) angular momentum of a charged particle with spin that moves in a Coulomb plus spin-orbit-coupling potential is conserved. In a classical nonrelativistic treatment of this problem, in which the Lagrange equations determine the orbital motion and the Thomas equation yields the…

Charges and fields in a straight, infinite, cylindrical wire carrying a steady current are determined in the rest frames of ions and electrons, starting from the standard assumption that the net charge per unit length is zero in the lattice frame and taking into account a self-induced pinch effect. The analysis presented illustrates the mutual…

In this paper we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulae, various approximations of the electron distribution are shown which facilitate the interpretation of the results.…

A detailed derivation of analytic solutions is presented for overlap, kinetic, nuclear attraction and electron repulsion integrals involving Cartesian Gaussian-type orbitals. It is demonstrated how s-type orbitals can be used to evaluate integrals with higher angular momentum via the properties of Hermite polynomials and differentiation with…

We discuss a quantum-mechanical model of two particles that interact by means of a harmonic potential and are confined to a one-dimensional box with impenetrable walls. We apply perturbation theory to the cases of different and equal masses and analyse the symmetry of the states in the latter case. We compare the approximate perturbation results…

The history of Laplace's equations for spherical and cylindrical droplets and the concept of dividing surface in Gibbs' thermodynamic theory of capillary phenomena are briefly reviewed. The existing theories of surface tensions of cylindrical droplets are briefly reviewed too. For cylindrical droplets, a new method to calculate the radius and the…

The photoelectric effect is widely taught in schools and institutions. It is common knowledge that in order for photoelectrons to be emitted, the energy of the incoming photons must be greater than the work function of the irradiated metal (i.e. hv greater than [phi][subscript emitter]). However, what may not be as commonly known is that the…

The performance of a fan is usually estimated using hydrodynamical considerations. The calculations are long and involved and the results are expressed in terms of three affinity laws. In this paper we use kinetic theory to attack this problem. A hard sphere collision model is used, and subsequently a correction to account for the flow behaviour…

Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…

The teaching of the different aspects of a sensor system, with a focus on the involved nanotechnology, is a challenging, yet important task. We present the development of an electronic nose system that utilizes a nanoscale amperometric sensing mechanism for gas mixtures. The fabrication of the system makes use of a basic microfabrication facility,…

Single and double electromagnetically induced transparencies (EIT) in a medium, consisting of four-level atoms in the inverted-Y configuration, are discussed using mechanical and electrical analogies. A three-coupled spring-mass system subject to damping and driven by an external force is used to represent the four-level atom mechanically. The…

We present a laboratory experiment that allows undergraduate or graduate students to get introduced to colloidal crystal research concepts in an interesting way. Moreover, such experiments and studies can also be useful in the field of crystallography or solid-state physics. The work concerns the growth of colloidal crystal thin films obtained…

The Young-Feynman two-hole interferometer is widely used to present electron wave-particle duality and, in particular, the buildup of interference fringes with single electrons. The teaching approach consists of two steps: (i) electrons come through only one hole but diffraction effects are disregarded and (ii) electrons come through both holes…

We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…

In this paper, we accurately estimate the ground-state energy and the atomic radius of the helium atom and a helium-like Hookean atom by employing the uncertainty principle in conjunction with the variational approach. We show that with the use of the uncertainty principle, electrons are found to be spread over a radial region, giving an electron…