Revisiting the Majorana Relativistic Theory of Particles with Arbitrary Spin

In 1932 Ettore Majorana published an article proving that relativity allows any value for the spin of a quantum particle and that there is no privilege for the half integer spin. The Majorana idea was so innovative for the time that the scientific community understood its importance only towards the end of the thirties. This paper aims to highlight the depth of the scientific thought of Majorana that, well in advance of its time, opened the way for modern particle physics and introduced for the first time the idea of a universal quantum equation, able to explain the behavior of particles with arbitrary spin and of any nature, regardless the value of their speed. It will be analyzed in detail and made explicit all the steps that lead to the physical mathematical formulation of the Majorana theory. A part of these steps require basic knowledge of quantum physics but not for this should be regarded as trivial since they show the physical meaning hidden into the structure of the equation. Moreover, the explicit method for the construction of the infinite matrices will be given, by which the infinite components of the wave functions representing the fundamental and excited states of the particle are calculated.Comment: Paper revised after publication on "Advances in Physics Theories and Applications", Vol. 48 (2015) - ISSN (Paper)2224-719X ISSN (Online)2225-063

Superluminal Tunneling of a Relativistic Half-Integer Spin Particle Through a Potential Barrier

This paper investigates the problem of a relativistic Dirac half integer spin free particle tunneling through a rectangular quantum-mechanical barrier. If the energy difference between the barrier and the particle is positive, and the barrier width is large enough, there is proof that the tunneling may be superluminal. For first spinor components of particle and antiparticle states, the tunneling is always superluminal regardless the barrier width. Conversely, the second spinor components of particle and antiparticle states may be either subluminal or superluminal depending on the barrier width. These results derive from studying the tunneling time in terms of phase time. For the first spinor components of particle and antiparticle states, it is always negative while for the second spinor components of particle and antiparticle states, it is always positive, whatever the height and width of the barrier. In total, the tunneling time always remains positive for particle states while it becomes negative for antiparticle ones. Furthermore, the phase time tends to zero, increasing the potential barrier both for particle and antiparticle states. This agrees with the interpretation of quantum tunneling that the Heisenberg uncertainty principle provides. This study results are innovative with respect to those available in the literature. Moreover, they show that the superluminal behaviour of particles occurs in those processes with high-energy confinement.Comment: 13 pages, 8 figure

A New Derivation of the Time-Dependent Schrödinger Equation from Wave and Matrix Mechanics

An alternative method is proposed for deriving the time-dependent Schrödinger equation from the pictures of wave and matrix mechanics. The derivation is of a mixed classical–quantum character, since time is treated as a classical variable, thus avoiding any controversy over its meaning in quantum mechanics. The derivation method proposed in this paper requires no ad hoc assumption and avoids going through a second-order differential equation that can be reduced to the well-known time-dependent Schrödinger equation only postulating a complex wavefunction with a time dependence given by , as did by Schrödinger in its original paper of 1926 [1]. Keywords: Schrödinger equation, wave–particle duality, Hermitian operators, commutation relation