The problem of two electrons in a three-dimensional quantum dot with Gaussian confinement is investigated for the singlet pairing by a variational method with a very simple wavefunction containing only a single parameter and a Jastrow-like factor, which is shown to yield fairly good results for deep confining potentials. The calculation is also performed for a few realistic semiconductor quantum dots and the phase diagrams for the two-electron singlet states are obtained for these materials. The pair density function is calculated for several parameter values and its peak positions are obtained as a function of the confinement length and the depth of the potential to study the behaviour of the electron-pair size. The size of the bound pair of electrons is also obtained by directly calculating the average distance between the two electrons in three different ways and compared with the pair correlation results. It is furthermore shown that, other properties remaining the same, the two-electron energy and the electron-pair size depend crucially on the effective electronic mass and the dielectric constant of the material. Finally, the ways of improving the wavefunction are also indicated.

We show that the electron–positron annihilation process ending with the creation of two gamma photons (with right- and left-hand circular helicity) can be explained in terms of the current loop model. We first show that both electron and positron (which are spin 1/2 particles) carry an intrinsic flux quantum of ±Φ0/2 even in the absence of an external magnetic field. By using the conservation of the magnetic flux quanta for collisions, we then argue that photon also carries a magnetic flux quantum of ±Φ0 = ±(hc/e) with itself along the propagation direction, where the (+) sign corresponds to the right-hand helicity and (-) one to the left-hand one.

In analogy with the fact that there are magnetic moments associated respectively with the electron's orbital and spin motion in an atom we present several analyses on a proposal to introduce a concept of intrinsic magnetic flux associated with the electron's orbital and spin motion. It would be interesting to test or to demonstrate Faraday's and Lenz's laws of electromagnetic induction arising directly from the flux change due to transition of states in an atom and to examine applications of this concept of intrinsic flux.KEY WORDS: electron intrinsic orbital and spin magnetic flux.

The flux associated with the electron's spin is calculated on a the basis of the magnetic top (spherical top) model which can be made equivalent to a circular current loop with radius R in x-y plane in the presence of a uniform magnetic field in z-direction. It is found that the flux associated with the electron's spin is exactly equal to +Φ 0 /2 for a spin down electron and −Φ 0 /2 spin up one.Keywords: Cyclotron period; magnetic flux; magnetic top model.where A is the vector potantial given by B = curl A. According to the Bohr-Sommerfeld relation, the orbits are quantized such as

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