Recently, there have been many efforts to use the research techniques developed in the field of physics education research to improve the teaching and learning of quantum mechanics. In particular, part of this research is focusing on misconceptions held by students. For instance, a set of misconceptions is associated with the concept of stationary states. In this paper, we argue that a possible way to remove these is to solve the Schrödinger equation using the evolution operator method (EOM), and stress the fact that to find stationary states is only the first step in solving that equation. The EOM consists in solving the Schrödinger equation by direct integration, i.e. Ψ(x, t) = U(t)Ψ(x, 0), where is the time evolution operator, and Ψ(x, 0) is the initial state. We apply the evolution operator method in the case of the harmonic oscillator.

The Heisenberg uncertainty principle, which underlies many quantum key features, is under close scrutiny regarding its applicability to new scenarios. Using both the Bell-Kochen-Specker theorem establishing that observables do not have predetermined values before measurements and the measurement postulate of quantum mechanics, we propose that in order to describe the disturbance produced by the measurement process, it is convenient to define disturbance by the changes produced on quantum states. Hence, we propose to quantify disturbance in terms of the square root of the Jensen-Shannon entropy distance between the probability distributions before and after the measurement process. Additionally, disturbance and statistical distinguishability of states are fundamental concepts of quantum mechanics that have thus far been unrelated; however, we show that they are intermingled thereupon we enquire into whether the statistical distinguishability of states, caused by statistical fluctuations in the measurement outcomes, is responsible for the disturbance’s magnitude.

To the quantum mechanics specialists community it is a well-known fact that the famous original Stern–Gerlach experiment (SGE) produces entanglement between the external degrees of freedom (position) and the internal degree of freedom (spin) of silver atoms. Despite this fact, almost all textbooks on quantum mechanics explain this experiment using a semiclassical approach, where the external degrees of freedom are considered classical variables, the internal degree is treated as a quantum variable, and Newton's second law is used to describe the dynamics. In the literature there are some works that analyze this experiment in its full quantum mechanical form. However, astonishingly, to the best of our knowledge the original experiment, where the initial states of the spin degree of freedom are randomly oriented coming from the oven, has not been analyzed yet in the available textbooks using the Schrödinger equation (to the best of our knowledge there is only one paper that treats this case: Hsu et al (2011 Phys. Rev. A 83 012109)). Therefore, in this contribution we use the time-evolution operator to give a full quantum mechanics analysis of the SGE when the initial state of the internal degree of freedom is completely random, i.e. when it is a statistical mixture. Additionally, as the SGE and the development of quantum mechanics are heavily intermingled, we analyze some features and drawbacks in the current teaching of quantum mechanics. We focus on textbooks that use the SGE as a starting point, based on the fact that most physicist do not use results from physics education research, and comment on traditional pedagogical attitudes in the physics community.

This paper explains and illustrates the application of the evolution operator method to solve problems in quantum mechanics. Currently, this method has been proposed as a useful way to overcome some misconceptions in quantum mechanics. To illustrate the method, we apply it to analyze and study the case of a quantum system inside an infinite square well potential (ISWP), and compare this result with that obtained using the traditional method. Also, we analyze the collapse and revival phenomenon in the ISWP. In this case, we argue that the usual approach to studying this effect requires one to extend the function’s domain to infinity; however, there has not been any assurance that this extension preserves the self-adjointness of the Hamiltonian operator. The self-adjointness of the Hamiltonian operator is a vital requirement to guarantee the uniqueness of the Schrödinger equation’s solution.