Télécharger Quantum Wave in a Box sur PC

         


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Quantum Wave in a Box Sur iTunes

- Watch both solution ψ(x,t) and free wave-packet curves evolve together in time and separate when entering non-zero potential energy region.  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.  - 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.  - 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.  - Animation shows gaussian wave-packet ψ(x,t) evolving with real-time evaluation of average velocity, kinetic energy and total energy.  A solution of this differential equation represents the motion of a non-relativistic particle in a potential energy field V(x).  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.  - Quantum system defined by mass, interval [a, b] representing the Box and (real) potential energy V(x).  In Quantum Mechanics the one-dimensional Schrödinger equation is a fundamental academic though exciting subject of study for both students and teachers of Physics.  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.  Actually the originally continuous x-spatial differential problem is discretized over a finite interval (the Box) while time remains a continuous variable.  When computing eigenvalues only, lowest energy levels of bound states (if any) with up to 10-digit precision.  Animation showing evolution in time of a gaussian wave-packet.  Maximum value of N depends on device’s RAM: up to 4000 when computing eigenvalues and eigenvectors, up to 8000 when computing eigenvalues only.  - Zoom in and out any part of the curves and watch how ψ(x,t) evolve locally.  Quantum Wave in a Box does it ! For a large range of values of the quantum system parameters.  - Diagonalization of hamiltonian matrix H gives eigenvalues and eigenfunctions.  - Listing of energy levels and visualisation of eigenwave-functions.  Schrödinger equation solver 1D.  - Toggle between clockwise and counter-clockwise evolution of ψ(x,t).  User defined potential V(x).  Diagonalization of hamiltonian matrix.  But very few solutions can be derived with a paper and pencil.