| Vývojář: | Michel Ramillon (3) | ||
| Cena: | Zdarma | ||
| Hodnocení: | 0 | ||
| Recenze: | 0 Napsat recenzi | ||
| Seznamy: | 0 + 0 | ||
| Body: | 0 + 4 (3.3) ¡ | ||
| App Store | |||
Popis
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.
Snímky obrazovky
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- Dnes: Zdarma
- Minimální: Zdarma
- Maximální: $2.99
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Vývojář
- Michel Ramillon
- Platformy: iOS Aplikace (3)
- Seznamy: 0 + 0
- Body: 0 + 7 ¡
- Hodnocení: 0
- Recenze: 0
- Slevy: 0
- Videa: 0
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Další informace
- Verze: 1.0.3
- ID: com.homeosoft.Quantum-Wave-in-a-Box
- Kategorie:
iOS Aplikace›Vzdělávání - OS:
iPad,iPhone,iOS 11.0 a vyšší - Velikost:
12 Mb - Podporovaný jazyk:
English - Hodnocení obsahu:
4+ - App Store Hodnocení:
3.3(4) - Aktualizováno:
- Datum vydání:
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