On modeling and visualizing single-electron spin motion

F. Suekane

Samuel Bernard-Bernardet, Benjamin Apffel

The spinorial ball is an interactive electronic device that we recently introduced to discuss the origin of spin-1/2 from the representation of the rotation group, without the framework quantum mechanics. Nevertheless, it can also be viewed as a macroscopic visualization of a quantum two-level system, and can thus be used to gain intuition on some generic features of qubits. In this article, we show how the ball can be used to fully visualize the evolution of a single qubit under arbitrary operators of SU(2). The Bloch sphere, the Hopf fibration, and the Berry phase can also be easily visualized and manipulated using this original device. We also discuss how the spinorial ball can be used to represent Hamiltonian evolution, and we describe an explicit mapping between the ball's motion and the evolution of a spin-1/2 system in arbitrary magnetic fields. An electronic implementation of projective measurement that matches the predictions of quantum mechanics is also proposed.

Hideo Tsuru, Takeshi Kobayashi

Wave packet motions of a single electron in harmonic potentials or a magnetic field are obtained analytically. The phase of the wave function which depends on both time and space is also presented explicitly. The probability density of the electron changes its width and central position periodically. These results are visualized using computer animation techniques.

P. Bruno

Gurcharn Singh Sandhu

Even after extensive research in Quantum Mechanics, we are still unable to visualize instant-to-instant motion of an electron in hydrogen atom. That is because in QM treatment, potential energy term has been mistakenly assumed to be time-independent instead of depending on the instant-to-instant varying position of the orbiting electron [1]. This has led to wrong and weird solutions for the electron motion in hydrogen atom. Before the advent of wave mechanics, Sommerfeld model of elliptical electron orbits was able to explain most features of hydrogen spectra, except for the features associated with electron spin and magnetic moment interactions. However, the Sommerfeld elliptical orbits were of kinematic origin and could not provide visualization of instant-to-instant dynamic motion of the orbiting electron. Contrary to the QM perspective, we find that central core of the electron behaves as a classical particle while its electrostatic field behaves as a wave phenomenon. As such an electron under Coulomb force moves strictly in accordance with Newtonian laws of motion. In this paper, we develop dynamic electron orbits in hydrogen atom by using energy and angular momentum conservation principle in central force field. We have shown that during photon emission, angular momentum of the orbiting electron is changed by ħ due to recoil action. This may be the origin of various quantization rules. During emission of a photon, elliptical orbit transitions are also computed and plotted. Orbit transition time is of the order of 10-16 seconds. We have extended this methodology to compute electron orbits in hydrogen molecular bond and computed the H2 bond energy.