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SIMO : MATLAB programming app
SIMO : MATLAB programming app Vs. Quantum Wave in a Box

SIMO : MATLAB programming app vs Quantum Wave in a Box Usage & Stats

~~~~~~~~~ Check out our FREE app Console, which is powered by SIMO's MATLAB interpreter. If you find Console useful, SIMO is definitely suitable for you. ~~~~~~~~~ SIMO is a feature-rich development environment for MATLAB. We have developed a version of MATLAB interpreter that works for commonly used language syntax and functions for beginners. [+] Who will find SIMO useful? - Students learning the basics of MATLAB. - Course instructors of fundamental MATLAB courses. - Individuals whose works do not depend on specialised toolboxes and advanced language syntax. [+] What is SIMO? - It is an integrated environment for running MATLAB. - It allows you to create, edit, and run MATLAB code on iOS devices. - Unlike other apps that compute on the cloud, it performs computation entirely locally on device. No internet connection is needed. You don't miss a single app feature even if you are offline. [+] What SIMO cannot do? - It does not completely replace MATLAB, as it has only a subset of built-in functions of MATLAB. - It does not support advanced features such as Simulink or creating user-interface. [+] One app, all platforms - You will be amazed at how much work you can do on a phone. The app is designed to let you work effectively on smaller screens. - The iPad app features a split-screen layout. You can enjoy a full-screen workspace, or work on two views simultaneously. - The iPad app runs on Macs with Apple silicon as well. Buy one app and it works on all of the platforms. [+] MATLAB interpreter - The interpreter works for language syntax that is essential to survive a MATLAB course. It provides the most commonly used built-in functions for learners. - The interpreter computes on your device locally. You will not miss a single app feature even if you go completely offline. - SIMO comes with a full set of documentation and user guides. It is offline accessible and full-text searchable. [+] Visualization tool - Plots are rendered in real-time using your device's computing power. Operations such as updating line attributes, pan and zoom are fast and responsive. - Stunning 3D plots are rendered by the device's GPU in real-time. Pan, zoom or rotate with multi-touch gestures, trackpad or keyboard shortcuts. - Plot attributes are editable through the built-in user-interface. You can improvise with different styles without entering a single line of code. [+] Command console - You can run one or many lines of code from the command console. It supports line numbering, auto-intent and syntax highlighting. - Search over thousand lines of output data instantly. You'll never get overwhelmed by the sea of numbers. - Output data are formatted automatically to fit the screen size or app window. Data are always neatly presented however you resize the app. [+] File manager - Files can be synced across all of your iCloud Drive enabled devices (iPhone, iPad, Mac). Or, you can store them locally on device. - Tons of files buried in tons of folders? No worries. The search feature will help you find an item instantly. - It has features you expect from a useful file manager. Add, copy, delete, duplicate, move, rename, sort and more. [+] Script editor - It has features you expect from a useful script editor. Syntax highlight, auto-indent, line numbers and more. - Search for a word in a script. Replace occurrences with another word. - Recent items are accessible from your finger tip. It is a useful feature for navigating through frequently accessed files.

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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.