Quantum Wave in a Box vs Atomizer AR

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.

Atomizer AR turns your iPhone or iPad into a portable quantum chemistry lab. Visualize atomic and molecular orbitals in 3D, render electron density clouds, and step into immersive WebXR augmented reality where molecules sit on your desk at real-world scale. — WHAT YOU CAN DO — • Explore atomic orbitals computed from real hydrogenic wavefunctions: 1s, 2p, 3d, 4f and beyond, with adjustable shell glow and Bohmian trajectory animation. • View any molecule's molecular orbitals (HOMO, LUMO, intermediates) computed via PySCF on the cloud, then rendered as interactive isosurfaces. • See ball-and-stick models in WebXR augmented reality. Tap "View in AR", point at a flat surface, place the molecule on a table, then pinch to scale and drag to rotate. • Pair your phone with the desktop using Atomizer Remote: enter a 4-letter code, then tilt your phone to control the on-screen molecule with your gyroscope. Live preview streams back to your phone in real time. • Browse 40+ molecules — water, glucose, caffeine, benzene, ammonia, ethanol, methane, sulfuric acid and more — with energy diagrams, dipole arrows, lone pairs (VSEPR) and MO correlation diagrams. • Calculate molar mass live from any chemical formula, including parenthesised groups like Ca(OH)₂ and (NH₄)₂SO₄, with per-element breakdown. • Balance equations, run stoichiometry, sketch molecules in 2D, and explore reaction pathways. — SUBSCRIPTIONS — Free: 5 molecule renders per period. All calculator tools and full periodic table. Californium Pass — $2.99/month. 50 renders monthly, priority compute queue. Einsteinium Pass — $6.99/month. Unlimited renders, GLTF export for AR/3D printing, protein visualization, priority support. Auto-renews unless cancelled at least 24 hours before the period ends. Cancel anytime in Settings → Apple ID → Subscriptions. Subscriptions sync across iPhone, iPad, and electronvisual.org. Privacy: https://electronvisual.org/privacy Terms: https://electronvisual.org/terms