Corrigendum: ‘A full quantum analysis of the Stern–Gerlach experiment using the evolution operator method: analysing current issues in teaching quantum mechanics’

Abstract

A full quantum analysis of the Stern-Gerlach experiment using the evolution operator method: analysing current issues in teaching quantum mechanics E Benítez Rodríguez, L M Arévalo Aguilar and E Piceno Martínez -Applying classical geometry intuition to quantum spin

Quantum Nonlocality and Quantum Correlations in the Stern–Gerlach Experiment

“…The SGE experiment is usually analyzed in most textbooks in a semiclassical way, where the external degrees of freedom are considered as classical variables, and its dynamics is thought of in terms of Newton’s second law [ 5 , 6 , 9 ]. However, in the scientific literature, we can find proposals that treat the external degrees of freedom (EDF) as a quantum variable giving a quantum description of the evolution of the EDF; see [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 13 ].…”

“…The SGE experiment is usually analyzed in most textbooks in a semiclassical way, where the external degrees of freedom are considered as classical variables, and its dynamics is thought of in terms of Newton’s second law [ 5 , 6 , 9 ]. However, in the scientific literature, we can find proposals that treat the external degrees of freedom (EDF) as a quantum variable giving a quantum description of the evolution of the EDF; see [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 13 ]. Nevertheless, in a recent paper, we gave a complete quantum treatment of the SGE [ 5 , 6 ], as it was originally thought of by Scully et al [ 9 ], by using the evolution operator method [ 21 , 22 , 23 , 24 , 25 ] and obtaining the solution to the Schrödinger equation; this allows us to see the quantum features of the EDF.…”

“…For the case of the evolution of an initial superposition state of the spin degree of freedom, we have the initial state: where and are constants obeying , and is the Gaussian wave packet: where is the width of the wave packet, is the position and is the wave vector. Then, the evolved state is given by: where ∇ is the vector differential operator, m is the mass of the particle, and g is the gyromagnetic ratio; see [ 5 , 6 ] for details. The magnetic field of the SGE is an inhomogeneous magnetic field of the form , with a constant and b the strength of the inhomogeneity of the field.…”

“…Although nowadays, a significant number of new proposals has arisen to enhance our general understanding of the way it works and its possible uses [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 ], nonetheless, after almost one hundred years since its inception, still, there is not a total understanding of how it works yet in terms of an entire quantum mechanical description [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 ]; also, see [ 17 ]. In fact, most research analyses and textbooks have regularly focused on an SGE’s semiclassical model [ 5 , 6 , 9 ]. As an example of new approaches, Boustimi et al gave a step forward by abandoning the usual magnets’ configuration producing a quadrupolar static magnetic field (by using just four bars) with the objective of modulating an atomic beam by means of an interference pattern [ 18 ]; see also [ 19 ].…”

“…Recently, we argued that the SGE could easily be used to introduce the concept of entanglement between the external and internal degrees of freedom in the teaching of quantum mechanics [ 5 , 6 ], to exemplify the entanglement generation between discrete and continuous variables and between pure and mixed states, as well. To show these properties of the SGE, we have used the evolution operator method [ 21 , 22 , 23 , 24 , 25 ]; to see an independent test of this method, see [ 26 , 27 ].…”