A new introductory quantum mechanics curriculum

Kohnle, Antje; Bozhinova, Inna; Browne, Dan E.; Everitt, Mark J.; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth

doi:10.1088/0143-0807/35/1/015001

Cited by 85 publications

(78 citation statements)

References 29 publications

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“…The targets for these activities are junior-or seniorlevel introductory quantum mechanics students, particularly those in "spins-first" courses. [6][7][8][9] The game also may be played before students learn the theory of quantum states and measurements as a qualitative introduction to these topics, for example as a teaser activity for a sophomore-level modern physics survey course 12,20 or an introductory quantum computing course for nonphysicists. 21 Students who understand quantum measurements will also benefit because the core of the game is a foundational and subtle question: How much infor-mation can we gain from a single quantum measurement?…”

Section: Learning Objectivesmentioning

confidence: 99%

“…6,7 This "spins-first" approach aims to teach quantum axioms in mathematically simpler finite Hilbert spaces before bringing in the complications of solving the wave equation. 8,9 This article describes: a simple two-level quantum system, how to simulate measurements on this system using a classical random number generator (RNG) such as dice rolls, and a two-player competitive game using this simulation. Although many excellent teaching-focused computer simulations of quantum mechanical systems, 10 and specifically two-level systems, [11][12][13][14] exist, the exercise here takes a different approach.…”

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A simple game simulating quantum measurements of qubits

Corcovilos

2018

American Journal of Physics

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Games are useful tools for introducing new concepts to students. This paper describes a competitive two-player game for sophomore students in a modern physics survey course or junior/senior students in an introductory quantum mechanics course to build intuition and quantitative understanding of the probabilistic nature of quantum measurements in two-level systems such as qubits or the Stern-Gerlach experiment. The goal of the game is to guess a quantum state secretly chosen from a given set in the fewest number of measurements. It uses twenty-sided dice or other classical random number generators to simulate quantum measurements. The Bloch vector formalism is introduced to give a geometric description of the quantum states and measurement outcomes. Several ready-to-use sets of quantum states are given, so readers can jump right in and try the game themselves without any prior knowledge of quantum mechanics. More advanced students can also use the game in suggested follow-up exercises to deepen students' understanding of quantum measurements and their statistical description.

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Section: Learning Objectivesmentioning

confidence: 99%

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confidence: 99%

A simple game simulating quantum measurements of qubits

Corcovilos

2018

American Journal of Physics

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“…Indeed, several prior studies have found that many advanced students struggle with the foundational issues in quantum mechanics including measurement (e.g., see [1][2][3][4][5][6][7][8][9][10][11][12]). Studies have focused on diverse pedagogical approaches for helping students learn quantum mechanics better (e.g., see [13][14][15][16][17][18][19][20][21][22][23][24][25][26]), and visualization tools such as QuVIS and QuTIP have been developed to help students develop intuition about quantum mechanical phenomena [23,24].…”

Section: Introductionmentioning

confidence: 99%

Investigating and improving student understanding of the probability distributions for measuring physical observables in quantum mechanics

Marshman

Singh

2017

Eur. J. Phys.

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A solid grasp of the probability distributions for measuring physical observables is central to connecting the quantum formalism to measurements. However, students often struggle with the probability distributions of measurement outcomes for an observable and have difficulty expressing this concept in different representations. Here we first describe the difficulties that upper-level undergraduate and PhD students have with the probability distributions for measuring physical observables in quantum mechanics. We then discuss how student difficulties found in written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of the probability distributions of measurement outcomes for physical observables. The QuILT strives to help students become proficient in expressing the probability distributions for the measurement of physical observables in Dirac notation and in the position representation and be able to convert from Dirac notation to position representation and vice versa. We describe the development and evaluation of the QuILT and findings about the effectiveness of the QuILT from in-class evaluations.

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“…Difficulties and misconceptions in learning such topics are well known and very often described [15,16]. Recent papers proposing novel approaches are still devoted to reduce such difficulties [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo method to explain the probabilistic interpretation of atomic quantum mechanics

Coto

Arencibia

Suárez

2016

Comp Applic In Engineering

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Quantum mechanics description of physical and chemical systems is included in books ofPhysics, General Chemistry or Physical Chemistry including mathematical, graphical, and conceptual descriptions. Mathematical calculations are complex and are covered only in advanced courses. Main problem in the first degree courses is the understanding of the probabilistic interpretation of quantum mechanics. The Monte Carlo method is based on probabilistic concepts and its application to quantum calculations can be carried out quite straightforward. In this work, a simple Monte Carlo method was used to obtain a sequence of random electron coordinates according to the probability given by the wave function. Electron is seen as a shot whose appearance is only accepted and plotted when probability is high enough. Hydrogen atom was studied as it is a familiar system for most students and its description can be easily related to previous knowledge of atomic orbitals. The objective of the present work is to supply all the crucial points that students need to create their own program to plot atomic orbitals according to the above ideas. All the numerical details are indicated in order to get the proposed programming project as a simple task. Student should be able to generate random electron coordinates, to compute wave functions and probabilities, and to obtain plots according to the right probabilistic interpretation of quantum mechanics. In order to show the quantitative obtained plots some results were shown. Typical s, p, and d orbitals were obtained and compared to the usual angular and radial representation. ß

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A new introductory quantum mechanics curriculum

Cited by 85 publications

References 29 publications

A simple game simulating quantum measurements of qubits

A simple game simulating quantum measurements of qubits

Investigating and improving student understanding of the probability distributions for measuring physical observables in quantum mechanics

Monte Carlo method to explain the probabilistic interpretation of atomic quantum mechanics

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