arXiv subjects

Luca Nanni

Publications and source records attributed to Luca Nanni.

25 records · Page 2Linked to original sources

arXiv2017

Wave Packet Dynamics in the Majorana Equation

In the Majorana equation for particles with arbitrary spin, wave packets occur due to not only the uncertainty that affects position and momentum but also due to infinite components with decreasing mass that form the Majorana spinor. In this paper, we prove that such components contribute to increase the spreading of wave packets. Moreover, Zitterbewegung takes place in both the time propagation of Dirac wave packets and in Majorana wave packets. However, it shows a peculiar fine structure. Finally, group velocity always remains subluminal and contributions due to infinite components decrease progressively as spin increases.

physics.gen-ph↗

arXiv2016

Space-Like Particle Production: an Interpretation Based on the Majorana Equation

This study reconsiders the decay of an ordinary particle in bradyons, tachyons and luxons in the field of the relativistic quantum mechanics. Lemke already investigated this from the perspective of covariant kinematics. Since the decay involves both spacelike and timelike particles, the study uses the Majorana equation for particles with an arbitrary spin. The equation describes the tachyonic and bradyonic realms of massive particles, and approaches the problem of how spacelike particles might develop. This method confirms the kinematic constraints that Lemke theory provided and proves that some possible decays are more favourable than others are.

physics.gen-ph↗

arXiv2016

Overcoming the Bradyon-Tachyon Barrier

In this study, the problem of overcoming the infinite energy barrier separating the bradyonic and tachyonic realms is investigated. Making use of the Majorana equation for particles with arbitrary spin and the Heisenberg uncertainty principle, it is proved that, under certain conditions of spatial confinement, quantum fluctuations allow particles with very small mass and velocity close to the speed of light to pass in the tachyonic realm, avoiding the problem of the infinite barrier. This theoretical approach allows an avoidance of the difficulties encountered in quantum field theory when it is extended to particles with imaginary rest mass.

physics.gen-ph↗

arXiv2016

A Discussion on the Heisenberg Uncertainty Principle from the Perspective of Special Relativity

In this note, we consider the implications of the Heisenberg uncertainty principle (HUP) when computing uncertainties that affect the main dynamical quantities, from the perspective of special relativity. Using the well-known formula for propagating statistical errors, we prove that the uncertainty relations between the moduli of conjugate observables are not relativistically invariant. The new relationships show that, in experiments involving relativistic particles, limitations of the precision of a quantity obtained by indirect calculations may affect the final result.

quant-ph↗

arXiv2015

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.

physics.hist-ph↗

arXiv2015

The Hydrogen Atom: a Review on the Birth of Modern Quantum Mechanics

The purpose of this work is to retrace the steps that were made by scientists of XX century, like Bohr, Schrodinger, Heisenberg, Pauli, Dirac, for the formulation of what today represents the modern quantum mechanics and that, within two decades, put in question the classical physics. In this context, the study of the electronic structure of hydrogen atom has been the main starting point for the formulation of the theory and, till now, remains the only real case for which the quantum equation of motion can be solved exactly. The results obtained by each theory will be discussed critically, highlighting limits and potentials that allowed the further development of the quantum theory.

physics.hist-ph↗

arXiv2015

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

An alternative method is proposed for deriving the time dependent Schroedinger 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 Schroedinger equation only postulating a complex wavefunction with an exponential time dependence, as did by Schroedinger in its original paper of 1926.

physics.gen-ph↗