Math Master:ArithmeticExplorer vs Quantum Wave in a Box Utilisation & Stats

*Unlock the world of numbers with Math Master: Arithmetic Explorer!* This engaging and interactive math app is designed to make learning arithmetic operations not just easy, but incredibly fun for learners of all ages. Dive into an endless adventure with addition, subtraction, multiplication, and division through a unique blend of guided learning and hands-on practice. *Features:* - *Customizable Quizzes:* With Math Master, you can take on a variety of randomly generated quizzes that challenge your arithmetic skills. Each quiz is tailored to keep you on your toes and help reinforce your mathematical knowledge. - *Flexible Range Setting:* Prepare for exams or simply challenge yourself by setting specific numerical ranges for your quizzes. Whether you're mastering the basics or pushing your limits, Math Master adapts to your level. - *Exam Paper PDF Generator:* Exclusive to Math Master is the innovative option to create your own question paper sets. This feature allows users to generate a series of questions within their chosen range and operation, making it an ideal tool for students, teachers, and parents looking to prepare for upcoming math exams. - *Engaging User Interface:* With a user-friendly design and intuitive navigation, Math Master makes learning arithmetic a joy. The app's vibrant graphics and responsive design ensure a smooth and enjoyable learning experience. - *Educational for All Ages:* Whether you're a young learner just starting out, a student brushing up on basics, or an adult revisiting arithmetic, Math Master offers a comprehensive and adaptable platform for enhancing your math skills. Join the thousands of users improving their math skills with Math Master: Arithmetic Explorer. It's not just an app; it's your gateway to becoming a math wizard. Download now and start your journey to arithmetic mastery today!
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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.
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Comparaison des classements Math Master:ArithmeticExplorer vs. Quantum Wave in a Box

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Math Master:ArithmeticExplorer VS.
Quantum Wave in a Box

19écembre d, 2024