# Quantum Wave in a Box > Numerical solver for 1D Schrödinger equation with user-defined potentials and wave-packet animation. (iPhone/iPad app by Michel Ramillon.) - Source: https://appshunter.io/ios/app/quantum-wave-in-a-box/id1179258292 (this page in markdown: same URL + `.md`) - Developer: [Michel Ramillon](https://appshunter.io/developer/1179258291) - Category: Education - Price: Free - Rating: 3.30/5 from 4 App Store ratings · 1 written reviews indexed - Age rating: 4+ - Requires: iOS 11.0 · 12 MB - Languages: American English - Released: 2017-01-01 - Data updated: 2026-06-01 - Monetization: free - User reviews in markdown: https://appshunter.io/ios/app/quantum-wave-in-a-box/id1179258292/reviews.md ## What is Quantum Wave in a Box? Schrödinger equation solver 1D. User defined potential V(x). Diagonalization of hamiltonian matrix. Animation showing evolution in time of a gaussian wave-packet. In Quantum Mechanics the one-dimensional Schrödinger equation is a fundamental academic though exciting subject of study for both students and teachers of Physics. A solution of this differential equation represents the motion of a non-relativistic particle in a potential energy field V(x). But very few solutions can be derived with a paper and pencil. Have you ever dreamed of an App which would solve this equation (numerically) for each input of V(x) ? Give you readily energy levels and wave-functions and let you see as an animation how evolves in time a gaussian wave-packet in this particular interaction field ? Quantum Wave in a Box does it ! For a large range of values of the quantum system parameters. Actually the originally continuous x-spatial differential problem is discretized over a finite interval (the Box) while time remains a continuous variable. The time-independent Schrödinger equation H ψ(x) = E ψ(x), represented by a set of linear equations, is solved by using quick diagonalization routines. The solution ψ(x,t) of the time-dependent Schrödinger equation is then computed as ψ(x,t) = exp(-iHt) ψ₀(x) where ψ₀(x) is a gaussian wave-packet at initial time t = 0. You enter V(x) as RPN expression, set values of parameters and will get a solution in many cases within seconds ! - Atomic units used throughout (mass of electron = 1) - Quantum system defined by mass, interval [a, b] representing the Box and (real) potential energy V(x). - Spatially continuous problem discretized over [a, b] and time-independent Schrödinger equation represented by a system of N+1 linear equations using a 3, 5 or 7 point stencil; N being the number of x-steps. Maximum value of N depends on device’s RAM: up to 4000 when computing eigenvalues and eigenvectors, up to 8000 when computing eigenvalues only. - Diagonalization of hamiltonian matrix H gives eigenvalues and eigenfunctions. When computing eigenvalues only, lowest energy levels of bound states (if any) with up to 10-digit precision. - Listing of energy levels and visualisation of eigenwave-functions. - Animation shows gaussian wave-packet ψ(x,t) evolving with real-time evaluation of average velocity, kinetic energy and total energy. - Toggle between clockwise and counter-clockwise evolution of ψ(x,t). - Watch Real ψ, Imag ψ or probability density |ψ|². - Change initial gaussian parameters of the wave-packet (position, group velocity, standard deviation), enter any time value, then tap refresh button to observe changes in curves without new diagonalization. This is particularly useful to get a (usually more precise) solution for any time value t when animation is slower in cases of N being large. - Watch both solution ψ(x,t) and free wave-packet curves evolve together in time and separate when entering non-zero potential energy region. - Zoom in and out any part of the curves and watch how ψ(x,t) evolve locally. ## Key features - Schrödinger equation solver (1D) - User-defined potential V(x) - Hamiltonian matrix diagonalization - Wave-packet evolution animation - Energy levels and wave-functions visualization - RPN expression input for V(x) ## Recent user reviews (1 of 1) All indexed reviews: https://appshunter.io/ios/app/quantum-wave-in-a-box/id1179258292/reviews.md ### 2/5 — Stopped working. *2018-05-29* Used to work great. Now crashes when loading and dumps back to home screen in one second. **Developer response:** Thanks for this feedback. When you update your device with a new release of iOS, the App may stop working. The code needs to be recompiled. This is what Apple does actually. I did download the App today and it works nice with the latest iOS 11.4. Even if it is still version 1.0.2 of Quantum Wave in a Box. I suggest you delete the App from your device then download it anew. Let me know if it solves the crashing problem and deserve maybe some additional stars. ## Frequently asked questions about Quantum Wave in a Box ### What is Quantum Wave in a Box used for? Quantum Wave in a Box is used to numerically solve the one-dimensional Schrödinger equation. It allows users to define potential energy fields and visualize the evolution of wave-packets, aiding in the study of quantum mechanics. ### How does Quantum Wave in a Box solve the Schrödinger equation? The app discretizes the continuous spatial problem and solves the time-independent Schrödinger equation using diagonalization routines. The time-dependent equation is then solved using the computed Hamiltonian and an initial Gaussian wave-packet. ### What kind of potentials can I input into Quantum Wave in a Box? You can input any real potential energy V(x) as an RPN expression. The app uses atomic units, and the quantum system is defined by mass, the interval of the box, and the potential energy function. ### Can I see how a wave-packet changes over time with Quantum Wave in a Box? Yes, the app provides an animation showing the evolution of a Gaussian wave-packet in time. You can observe its movement, changes in kinetic and total energy, and its interaction with the defined potential. ### What are the limitations of Quantum Wave in a Box regarding system size? The maximum number of x-steps (N) depends on your device's RAM. It can go up to 4000 steps when computing eigenvalues and eigenvectors, and up to 8000 steps when computing only eigenvalues. ### Does Quantum Wave in a Box have ads? No, Quantum Wave in a Box does not contain advertisements. It is a free application designed for educational purposes without any ad interruptions. ### What devices is Quantum Wave in a Box compatible with? Quantum Wave in a Box is available for iPhone, iPad, and iPod devices. It is designed to run on Apple's mobile operating system. ### How often is Quantum Wave in a Box updated? The latest version of Quantum Wave in a Box is 1.0.3, last updated on January 8, 2023. The app was initially released on January 1, 2017. ## Version history (last 3 releases) ### 1.0.3 — 2023-01-08 Update for iOS 16. ### 1.0.2 — 2017-01-27 This app has been updated by Apple to display the Apple Watch app icon. - Language: english (previously appeared mistakenly as french). - Fixes an issue encountered when trying to access Photos. - Optimisation of successive graphic actions for repeated taps on HOME button. ### 1.0 — 2016-12-21 No release notes. ## Apps similar to Quantum Wave in a Box | App | Rating | Price | Category | | --- | --- | --- | --- | | [Matrix-Analysis](https://appshunter.io/ios/app/matrix-analysis/id1619005601) | — | Free | Education | | [EMwaveRT](https://appshunter.io/ios/app/emwavert/id1387286837) | — | Free | Education | | [Atomizer AR: Quantum Chemistry](https://appshunter.io/ios/app/atomizer-ar-quantum-chemistry/id6449015706) | 4.0 (3) | Free | Education | | [Least Squares Curve Fit](https://appshunter.io/ios/app/least-squares-curve-fit/id6443509668) | 5.0 (2) | Free | Education | | [영 단어즙](https://appshunter.io/ios/app/id1480979760) | 5.0 (1) | Free | Education | | [Solis USA States and Capitals](https://appshunter.io/ios/app/solis-usa-states-and-capitals/id1479512480) | — | Free | Education | ## More apps by Michel Ramillon - [Homeorep](https://appshunter.io/ios/app/homeorep/id1257014803) - [Boger](https://appshunter.io/ios/app/boger/id1422598028) All apps by Michel Ramillon: https://appshunter.io/developer/1179258291 --- *Data collected daily from the US App Store and indexed by [AppsHunter](https://appshunter.io/). User reviews are verbatim App Store reviews. Ratings, prices and chart positions refresh continuously; this snapshot is from 2026-06-01.*