Quantum Wave in a Box 4+
Michel Ramillon
Designed for iPad

 Free
Screenshots
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 wavepacket.
In Quantum Mechanics the onedimensional 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 nonrelativistic 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 wavefunctions and let you see as an animation how evolves in time a gaussian wavepacket 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 xspatial differential problem is discretized over a finite interval (the Box) while time remains a continuous variable. The timeindependent 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 timedependent Schrödinger equation is then computed as ψ(x,t) = exp(iHt) ψ₀(x) where ψ₀(x) is a gaussian wavepacket 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 timeindependent Schrödinger equation represented by a system of N+1 linear equations using a 3, 5 or 7 point stencil; N being the number of xsteps. 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 10digit precision.
 Listing of energy levels and visualisation of eigenwavefunctions.
 Animation shows gaussian wavepacket ψ(x,t) evolving with realtime evaluation of average velocity, kinetic energy and total energy.
 Toggle between clockwise and counterclockwise evolution of ψ(x,t).
 Watch Real ψ, Imag ψ or probability density ψ².
 Change initial gaussian parameters of the wavepacket (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 wavepacket curves evolve together in time and separate when entering nonzero potential energy region.
 Zoom in and out any part of the curves and watch how ψ(x,t) evolve locally.
What’s New
Version 1.0.3
Update for iOS 16.
App Privacy
The developer, Michel Ramillon, indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy.
Data Not Collected
The developer does not collect any data from this app.
Privacy practices may vary based on, for example, the features you use or your age. Learn More
Information
 Provider
 Michel Ramillon
 Size
 12.1 MB
 Category
 Education
 Compatibility

 iPhone
 Requires iOS 11.0 or later.
 iPad
 Requires iPadOS 11.0 or later.
 iPod touch
 Requires iOS 11.0 or later.
 Mac
 Requires macOS 11.0 or later and a Mac with Apple M1 chip or later.
 Apple Vision
 Requires visionOS 1.0 or later.
 Languages

English
 Age Rating
 4+
 Copyright
 © 20152023 Michel Ramillon
 Price
 Free