Quantum Wave in a Box 1.0.3
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Free Version
Publisher Description
Schrödinger's equation solver 1D with user defined potential. Evolution with time of a gaussian wave packet.
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.
Jan 8, 2023
Version 1.0.3
Update for iOS 16.
About Quantum Wave in a Box
Quantum Wave in a Box is a free app for iOS published in the Kids list of apps, part of Education.
The company that develops Quantum Wave in a Box is Michel Ramillon. The latest version released by its developer is 1.0.3.
To install Quantum Wave in a Box on your iOS device, just click the green Continue To App button above to start the installation process. The app is listed on our website since 2023-01-08 and was downloaded 25 times. We have already checked if the download link is safe, however for your own protection we recommend that you scan the downloaded app with your antivirus. Your antivirus may detect the Quantum Wave in a Box as malware if the download link is broken.
How to install Quantum Wave in a Box on your iOS device:
- Click on the Continue To App button on our website. This will redirect you to the App Store.
- Once the Quantum Wave in a Box is shown in the iTunes listing of your iOS device, you can start its download and installation. Tap on the GET button to the right of the app to start downloading it.
- If you are not logged-in the iOS appstore app, you'll be prompted for your your Apple ID and/or password.
- After Quantum Wave in a Box is downloaded, you'll see an INSTALL button to the right. Tap on it to start the actual installation of the iOS app.
- Once installation is finished you can tap on the OPEN button to start it. Its icon will also be added to your device home screen.
