The Quantum Mechanics Visualisation Project

The latest simulation (the second with the new design!) "The variational method" allows you to estimate ground state energies and eigenfunctions using trial functions ψ_α(x) that depend on a parameter α. You can record your estimates for three different potential energies and compare how well the different trial functions fare. As usual, there is a second Challenges tab.

Welcome to the new design of the simulations! The latest simulation "Quantum and classical uncertainties" allows you to explore quantum uncertainty, errors due to instrumental imperfections and statistical errors in a Stern-Gerlach experiment using spin 1/2 and spin 1 particles. The new design also has some new features! The simulation now has drop-down panels, and the Challenges include a Hint button.

The website now includes a new HTML5 simulation on "Degenerate perturbation theory: 2D oscillator perturbation " The simulation considers the two degenerate first-excited states of a two-dimensional harmonic oscillator under the action of a perturbation that can be rotated in the xy-plane. Users can display graphs depicting the original and good basis states, the individual matrix elements of the matrix representing the perturbation, and the perturbed states. The simulation also includes challenges aligned with the learning goals.

The website now includes nine further activites for HTML5 simulations, including "Quantum key distribution (BB84 protocol) with spin 1/2 particles", "Fermions and bosons in a one-dimensional infinite square well", "Time-development of a free particle Gaussian wave packet", "Bloch sphere representation of quantum states for a spin 1/2 particle", "Time development of two-level quantum states in the Bloch sphere", "Successive measurements in the Bloch sphere representation", "Comparison of the half-harmonic and harmonic quantum oscillator", "Comparison of the finite and infinite square wells" and "Interferometer experiments with photons, particles and waves". These activities have been used with students at the University of St Andrews and in some cases also external institutions. Instructors are welcome to modify activities as needed to suit their context.

The website now includes a simulation on "Interferometer experiments with photons, particles and waves " that has been recoded in HTML5. This simulations is also incorporated in the UK Institute of Physics Quantum Physics resources at quantumphysics.iop.org. The simulation allows users to compare and contrast the behaviour of single photons with classical particles and electromagnetic waves in the same interferometer setup, that includes one or two beamsplitters, a phaseshifter, two detectors and a coincidence counter. We have also extended the German part of the website to include translated versions of the "Interferometer experiments with photons, particles and waves" and "Entangled spin 1/2 particle pairs versus hidden variables" simulations.

The newly developed "Comparison of the finite and infinite square wells" simulation allows users to explore how the depth of a one-dimensional finite well effects the shapes of the energy eigenfunctions and the energy eigenvalues. Users can change the well depth and display the fraction of the probability density beyond the edges of the well. A second tab includes multiple challenges, e.g. considering how the well depth effects the energy of a particular excited state.

The newly developed "Comparison of the half-harmonic and harmonic quantum oscillator" simulation allows users to compare and contrast the energy eigenfunctions and energy eigenvalues of a one-dimensional harmonic oscillator and a half-harmonic oscillator which only has a parabolic potential energy for positive values of position. Users can change the quantum number and the frequency of the oscillator. A second tab includes multiple challenges, e.g. considering the differences in normalization between the two systems.

The website now includes three simulations on the Bloch sphere that have been recoded in HTML5. These simulations are also incorporated in the UK Institute of Physics Quantum Physics resources at quantumphysics.iop.org. The simulations include the "Bloch sphere representation of quantum states for a spin 1/2 particle", "Time development of two-level quantum states in the Bloch sphere", and "Successive measurements in the Bloch sphere representation". These simulations show how a spin 1/2 quantum state can be mapped to a point on the Bloch sphere, and the time evolution of the spin state on the Bloch sphere for a uniform magnetic field oriented along the z-direction.

The website now includes four further activites for HTML5 simulations, including "Probabilistic analysis of a block on a track", "The one-dimensional particle in a box", "Energy corrections in a perturbed infinite well" and "Successive energy measurements". These activities have been used with students at the University of St Andrews and in some cases also external institutions. Instructors are welcome to modify activities as needed to suit their context.

We have added activities for seven of the HTML5 simulations to the website, including "Energy uncertainty of quantum states", "Probability density and probability current", "Superposition states in an infinite square well", "Expansion in eigenstates", "Energy eigenfunctions of the two-dimensional infinite well", "Quantum key distribution using polarized photons", and "Density matrices for a two-level spin system". These activities have been used with students at the University of St Andrews and in some cases also external institutions. The activities can be accessed by clicking on the pdf symbol below the thumbnail images. Instructors are asked to email quvismail@st-andrews.ac.uk to obtain the password to download activity solutions via the lock symbol below the thumbnail images. Instructors are welcome to modify activities.

The newly developed "Time-development of infinite well quantum states" simulation targets a topic in quantum mechanics often found to be difficult. The simulation shows the time development of the wave function as a rotation in the complex plane and shows how the magnitude of the wave function at a particular point in the well is determined. Users can choose to display the ground state, first excited state or a superposition state in the infinite square well. A second tab includes multiple challenges e.g. determining the angular frequency of rotation of an energy eigenfunction in the complex plane.

A new simulation is available in the HTML5 collection. The "Probabilistic analysis of a block on a track" simulation allows users to take photos at random times of the position of a block on a track divided into two regions. Users can change the height and width of the track regions, and display the probability density of the resulting position distribution and the probabilities of finding the block in the two regions. A second tab includes multiple challenges, e.g. setting up a track for which the theoretical probability density is greater in the left region, but the theoretical probability of finding the block is smaller in this region. We have also made minor updates to the "Entanglement: The nature of quantum correlations" simulation based on outcomes of evaluation with students.

The newly developed "Spin precession" simulation allows users to explore how a uniform magnetic field region of varying length can induce spin flips in a stream of spin 1/2 particles. The simulation allows users to send spin 1/2 particles through an experiment consisting of a uniform magnetic field in between two Stern-Gerlach apparatuses which can be jointly rotated. A second tab includes multiple challenges, e.g. setting up configurations with particular spin flip probabilities. We have also made minor updates to the "Energy eigenfunctions of the two-dimensional infinite well", "Successive energy measurements" and "Interferometer experiments with single photons" simulations based on outcomes of evaluation with students.

The newly developed "Time-development of a free particle Gaussian wave packet" simulation allows users to explore how the amplitude and position uncertainty of the wave packet changes as it travels, and how the momentum uncertainy affects how quickly the wave packet spreads. Users can choose the initial position uncertainty of the wave packet and display graphs of the position and momentum uncertainty as a function of time. A second tab includes multiple challenges, e.g. comparing properties of two wave packets or determining a wave packet's group velocity. We have also updated the "Energy uncertainty of quantum states" simulation based on outcomes of evaluation with students.

The newly developed "One-dimensional particle in a box" simulation displays the wavefunction and probability density for a quantum particle confined to one dimension in an infinite square well (the so-called particle in a box). Users can select the energy level of the quantum state, change the width of the box, and choose a region over which the probabiity of finding the particle is then displayed. A second tab includes multiple challenges. We have also updated the simulations "Energy eigenfunctions of the two-dimensional quantum oscillator" and "Expansion in eigenstates" based on outcomes of evaluation with students.

A new simulation is available in the HTML5 collection. In the "Fermions and bosons in an infinite well" simulation, users can explore differences in the wave functions and probability densities for two-particle quantum states in a one-dimensional infinite square well. Users can choose to display distinguishable particles, indistinguishable fermions with parallel spins or indistinguishable spinless bosons and can swap the particles. A second tab contains multiple Challenges.

A new simulation is available in the HTML5 collection. In the "Energy shifts in an infinite well" simulation, users can choose different perturbations of an infinite square well and vary the perturbation strength. The unperturbed and perturbed energy levels are depicted. The simulation also shows graphically how the energy shift is calculated as the inner product of the unperturbed probability density and the perturbation. A second tab contains a Perturbation Game, where users need to perturb a well so that a particle in the well absorbs photons of a given energy.

A new simulation is available in the HTML5 collection. In the "Density matrix" simulation, users can view the quantum states and density matrices at various points in a Stern-Gerlach experiment.

Two new simulations are available in the HTML5 collection. In the "Quantum key distribution (BB84 protocol) using polarized photons" simulation, users can help two observers, Alice and Bob, generate a secure key using polarized photons sent from Alice to Bob and determine whether an eavesdropper has infiltrated their experiment. The "Energy eigenfunctions of the two-dimensional infinite well" simulation allows users to compare the energy eigenfunctions and associated probability densities for a quantum particle in a two-dimensional infinite square well and a rectangular well.

Three new simulations are available in the HTML5 collection. The "Expansion in eigenstates" simulation shows the expansion in eigenstates for different superposition states in an infinite square well. A second tab includes an Expansion Game where users can match a given superposition state as closely as possible by adjusting the expansion coefficients. The "Superposition states in an infinite well" simulation allows users to set up different superposition states in a one-dimensional infinite square well, and depicts the time development of the probability density, the expectation value of position and the position uncertainty. The "Successive energy measurements" simulation allows users to set up an energy eigenstate or a superposition state in an infinite square well or a harmonic oscillator potential and then take successive energy measurements.

Three new simulations are available in the HTML5 collection. The "Probability density and probability current" simulation allows users to explore the relation between these two quantities using a superposition state in a one-dimensional infinite square well. In the "Energy uncertainty of quantum states" simulation, users can set up different energy superposition states and display the expectation value of energy and the energy uncertainty. The "Quantum eraser" simulation is a single photon lab where polarizers with different orientations and a phase shifter can be dragged into a Mach-Zehnder interferometer. Users can explore how the position and the orientation of the polarizers determine whether or not single photon interference is observed. We have also added activities for six of the HTML5 simulations, namely Hidden variables (I) and (II), Superposition states, Spin-1 particles, Quantum cryptography (BBM92) and Entanglement. The activities can be accessed by clicking on the pdf symbol below the thumbnail images. Instructors are asked to email quvismail@st-andrews.ac.uk to obtain the password to download activity solutions.

Three new simulations are available in the HTML5 collection. In the "Quantum key distribution (BB84 protocol) with spin 1/2 particles" simulation, users can help two observers, Alice and Bob, generate a secure key using spin 1/2 particles sent from Alice to Bob and determine whether an eavesdropper has infiltrated their experiment. This simulation includes challenges as a second tab. The simulations "Entangled spin 1/2 particle pairs and hidden variables" and "Entangled spin 1/2 particle pairs versus an elementary hidden variable theory" allow users to assess whether a simple hidden variable theory would agree with measurement outcomes predicted by quantum theory. These simulations show a source of particle pairs in the middle of two Stern-Gerlach experiments. When the main controls are set to "Quantum theory", the particles pairs are entangled; when they are set to "Hidden variable theory", the particles have pre-determined definite measurement outcomes.

Welcome to the new QuVis website! The URL is unchanged at "www.st-andrews.ac.uk/physics/quvis". The new layout aims to make it easier for users to find simulations on topics of interest. It includes a left-hand navigation menu to select simulations on different topics and for different levels, and a search box in the top navigation panel. The older Flash simulations have been grouped into a single collection and can be accessed via the top "Flash Simulations" button. The HTML5 simulations are now the default collection and can be accessed via the "Home" and "HTML5 Simulations" buttons. The accompanying activities, activity solutions (password-protected) and simulations can be downloaded by clicking the small icons below the simulation thumbnails. Instructors wishing to obtain the password for the activity solutions are asked to email Antje Kohnle. The new website also includes a "Donate" option. The QuVis simulatios are freely available for anyone to use but expensive to make. Our key mission is to allow QuVis to remain a free, open and comprehensive collection to support learners, instructors and citizens around the world. Please help us achieve these goals by supporting QuVis. More information is available on the "Why donate?" page.

For German-speaking users, QuVis is pleased to announce that 11 simulations from the HTML5 collection are now available as German translations. The German versions can be accessed via the "Language" option using the left-hand navigation. Simulations available include "Quanten Schlüsselverteilung mit verschränkten Spin-1/2-Systemen", "Quanten Schlüsselverteilung (BB84 Protokoll) mit Spin-1/2 Teilchen", "Quanten Bombentest", "Einzelphotonen Labor", "Teilchen im unendlich hohen Potentialtopf", "Statistische Betrachtung eines Federpendels", "Statistische Messung", "Reine und gemischte Zustände", "Unbestimmtheit bei Spin-Messungen", "Stern-Gerlach Experimente mit Spin-1 Teilchen" and "Graphische Darstellung von Eigenvektoren". Torsten Franz of the Technical University of Braunschweig translated the majority of the German texts.

Recent additions to the HTML5 collection include a new "Quantum Cryptography" simulation where users can help two observers, Alice and Bob, determine whether an eavesdropper has infiltrated their experiment, a simulation on "Superposition States and Mixed States" where users can experimentally distinguish between quantum superposition states and classical mixed states, and a simulation on "Spin 1 Particles".

QuVis received the 2015 Physics Classics award of the Multimedia Educational Resources for Learning and Online Teaching (MERLOT, www.merlot.org ). Every year each of the MERLOT Editorial Boards selects an outstanding resource from its discipline to receive the MERLOT Classics Award. MERLOT considers this learning material an exemplary online learning resource and recognises it as such on its website.

The latest addition to our HTML5 collection is a simulation on "Entanglement: the nature of quantum correlations". This simulations allows users to create a particle pair spin state and take measurements to determine the correlation coefficient, and thus assess in what ways entangled states differ from non-entangled states.

Recent additions to the HTML5 collection include a new "Quantum Bomb Detection game" where users can save working bombs and recycle defective ones using the principle of interaction-free measurement, and an animation on "Matrix Multiplication" where users can choose from different matrices and change their numerical values. We have also updated the simulation "Interferometer experiments with single photons" based on outcomes of evaluation with students.