[en] It is suggested that the structure of space-time can be studied from the invariance of c and h with cosmic time

[en] By considering the allowed values of the z-component of the quantum mechanical angular momentum operator, a simple explanation is given for the term l(l+1)

[en] It is pointed out that the formula for the upward acceleration of a submerged, buoyant sphere should contain the effective mass of the water that is accelerated downward

[en] The availability of powerful microcomputers with graphics capabilities expands the range of numerical procedures that can be employed for undergraduate use. The use of simple software packages for the evaluation of multidimensional WKB approximate eigenvalues is discussed. Introductory courses in quantum mechanics rarely make use of semiclassical theories, such as WKB, to relate quantum mechanics to classical mechanics. This relationship can be helpful for the student's understanding of quantum mechanics, and a computer experiment can provide a useful avenue for making the concepts concrete. The major components of the approach involve the use of a package for the integration of differential equations, to treat the classical equations of motion, and a computer-aided design package to determine the phase integral areas. The codes are not expensive, and all exploit the graphical capabilities of microcomputers, which are critical for visualizing the relationship between classical and quantum ideas

[en] We give some illustrations and interpretations of supersymmetry in quantum mechanics in simple models. We show that the value of 2 for the g factor of the electron expresses the presence of supersymmetry in the Hamiltonian for an electron in a uniform magnetic field. The problem is considered both in the Schroedinger and Dirac formulations. We also show that the radial Coulomb problem with orbital angular momentum l, nuclear charge Z, and principal quantum number n, is supersymmetrically linked to the similar problem with charge Z(1-1/n) and quantum number n-1. Thereby the dependence of Coulomb energies only on the combination Z/n is seen as a manifestation of the supersymmetry in the radial Coulomb problem. Other examples of supersymmetry we consider are the Morse potential, the three-dimensional isotropic oscillator, the states of the helium atom and those of the hydrogen atom in an extremely strong magnetic field

[en] A unified description is presented for internal space-time symmetries of photons and neutrinos. Lorentz-boosted Dirac equation for a massive spin-1/2 particle is discussed in the Weyl representation. In the large-momentum/small-mass limit, the resulting large component of the Dirac spinor becomes invariant under transformations of the E(2)-like little group, and the small component is not invariant under the E(2)-like transformation. The gauge dependence of the photon four-potential can thus be derived from a direct product of the gauge-independent large component and the gauge-dependent small component

[en] The authors discuss an alternative method of performing coupling constant perturbation expansions in nonrelativistic quantum mechanics. This method, called logarithmic perturbation theory, yields new expressions for any-order corrections E/sub n/ to an unperturbed bound-state energy which do not involve cumbersome sums over intermediate unperturbed states. In one dimension, these corrections E/sub n/ can be evaluated using a simple explicit form containing a small number of integrals. In more than one dimension the approach is systematic but computations require the solution of well-defined partial differential equations. For order n = 2 this equation is identical to that appearing in the method of Dalgarno and Lewis. Numerous illustrative examples are presented. 5 references

[en] To dispel a widespread but erroneous belief among physicists that the penetration of ac magnetic fields into normal metals is determined by the usual skin depth δ alone, a simple analysis is presented of two problems in each of which a different length scale determines the effective screening. For a cylindrical can of thickness d<<δ and radius R<<λ, where λ is the wavelength, it is shown that the critical thickness for effective screening is d/sub c/ = δ²/R. For a planar film with thickness d<<δ, d/sub c/ = c/2πσ, where σ is the conductivity. An exact analysis is also presented of the screening for a cylinder of arbitrary thickness, as well as an analogy between screening by normal metals and screening by superconductors

[en] Rapid interstellar travel by means of spacetime wormholes is described in a way that is useful for teaching elementary general relativity. The description touches base with Carl Sagan's novel Contact, which, unlike most science fiction novels, treats such travel in a manner that accords with the best 1986 knowledge of the laws of physics. Many objections are given against the use of black holes or Schwarzschild wormholes for rapid interstellar travel. A new class of solutions of the Einstein field equations is presented, which describe wormholes that, in principle, could be traversed by human beings. It is essential in these solutions that the wormhole possess a throat at which there is no horizon; and this property, together with the Einstein field equations, places an extreme constraint on the material that generates the wormhole's spacetime curvature: In the wormhole's throat that material must possess a radial tension tau₀ with the enormous magnitude tau₀∼ (pressure at the center of the most massive of neutron stars) x (20 km)²/(circumference of throat)². Moreover, this tension must exceed the material's density of mass-energy, rho₀c². No known material has this tau₀>rho₀c² property, and such material would violate all the ''energy conditions'' that underlie some deeply cherished theorems in general relativity. However, it is not possible today to rule out firmly the existence of such material; and quantum field theory gives tantalizing hints that such material might, in fact, be possible

[en] This article is a ''sampler,'' which shows how quantum mechanics may be presented to students in a way that makes apparent how natural quantum mechanics is as a description of the world. The mathematical machinery of Hilbert space, the idea of representing observables by operators, the Schroedinger equation, and the position-momentum uncertainty relation all follow from natural assumptions that students can readily accept. The basic ideas of quantum mechanics are developed from intuitive first principles to the point where one can connect with more traditional treatments of quantum mechanics