Quantum Wave in a Box下载 - Quantum Wave in a Box苹果应用下载

基本信息

更新日期:: 2023-07-03
版本:: 1.0.2
大小:: 15.5 MB
类型:: 教育
平台:: iOS

评分:
发布日期:: 2017-01-27
价格:: ¥18
开发者:: Michel Ramillon

Quantum Wave in a Box应用截图

Quantum Wave in a Box应用简介

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.