MathStudio vs Quantum Wave in a Box Usage & Stats
MathStudio brings unprecedented computational power to your iPhone, iPad and Apple Watch. From building simple algorithms to creating interactive plots and animations, MathStudio bridges the gap between technology and your imagination.
"It is a programming tour-de-force, and really does provide a substantial subset of the functionality of desktop powerhouses like Mathematica and Maple."
▸ Simply the best calc app by ilachina
Develop your ideas to their fullest extent with MathStudio's expressive scripting language that features new syntax to do amazing things with just a few lines of code. Research and development in the scientific, engineering, mathematical and computing fields almost always involves the need for a scripting language to take your results one step further. Sync your documents with iCloud and have access from any device including your Mac.
"Perfect app for quick, powerful computation and visualization. I keep using it instead of Mathematica on my home computer because it's just so convenient. I can't believe how well it renders the evolution of such complex systems. I am blown away."
▸ Mini Mathematica by Professor Dave
MathStudio goes beyond a traditional graphing calculator by combining the power of the fastest proprietary computer algebra system available on iOS that can create cartesian, parametric, polar, implicit, vector fields, cylindrical, spherical, regression and image plots. Plot time graphs using the T variable to create animated plots that graph in space and time!
"This app really goes beyond your typical graphing calculator as well. How? By allowing you to interact with the graphs that you generate by touching them! I could go on and on about this app, but If you're still reading this review, let's just say that you're probably not going to find a better graphing calculator than this in the App Store."
▸ Replace your old graphing calculator! by AppShouter
From basic calculations to college calculus, MathStudio is a full featured scientific calculator and is an indispensable tool for students, teachers and engineers. It provides features that go beyond what you will find in traditional TI calculators with a modern and intuitive interface with hundreds of mathematical functions that cover Basic Math, Pre-Algebra, Algebra, Trigonometry, Precalculus, Calculus, Statistics, Finite Math and Linear Algebra.
"This app is way more than a graphing calculator. Capabilities like solving differential equations, preforming matrix factorizations and many more place it in a league of its own for hand held computation. The interface is simple and the extensive catalog makes it easy to quickly learn how to execute any operation. As an undergraduate math and physics student, this app has completely replaced my TI and drastically reduced the time I spend on MATLAB and Mathematica. I would recommend MathStudio to anyone!"
▸ Amazing Capabilities by Mac-Lover
From unit conversions to compound unit arithmetic, MathStudio includes complete support for units with intuitive syntax. Plot lists of data with powerful regression analysis functions, invert and multiply matrices, calculate determinants, solve derivatives, integrals, limits, differential equations and more with the most powerful computing app available on iOS.
"This app offers so much, and everyone can learn from it. Amazing 3D graphics, intuitively designed with the end user in mind. It is apps such as MathStudio, that show us why the App Store for iPhone/iPod Touch/iPad is by far the best for mobile devices."
▸ Creatively genius by howwaya
Are you a user from Mathematica or MATLAB? MathStudio offers much of the same functionality! For more help getting starting using MathStudio visit our discussion forums.
http://discuss.mathstud.io
- Apple App Store
- Paid
- Education
Store Rank
- -
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.
- Apple App Store
- Free
- Education
Store Rank
- -
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MathStudio VS. 
Quantum Wave in a BoxJanuary 12, 2026