iPhasematch vs Quantum Wave in a Box

iPhasematch allows you to calculate the phasematching condition of nonlinear wavelength conversion such as SHG or SFM based on published Sellmeier equiations. Downconversion (OPO) can be figured out by the reverse of SFM. It is a subset of the 'Qmix' function of a famous Windows software SNLO by Dr. Arlee Smith. This App does some of what SNLO does on your iOS device. It takes the crystal, two input wavelengths, and temperature and gives the phasematching orientations, effective nonlinear optical coefficients, walk-off angles, angular tolerance and temperature tolerance. In case of SHG, it also gives spectral tolerance. In biaxial crystals, it gives only the phasematching orientations in the principal planes, i.e., either theta=90 deg. or phi=0 or 90deg. Currently supported crystals: BBO, BiBO, CBO, CLBO, LB4, LBO, KBBF, KDP, KD*P, KN, KTP, Mg:LN, Mg:sLN, RBBF, RTP, YAB. NOTE: dn/dT data for LB4 was picked up from discrete data points in the reference and linearly extrapolated. Interface should be intuitive, giving phasematching with a tap of "PM" button,refractive index with "index" button and group index with "Gp.Idx" button, for the given condition (crystal, wavelengths, and temperature). DISCLAIMER: I cannot be held responsible for the result of the calculation it gives. I make every effort to make it accurate, and bug-free, but there could be errors in code. Please just use this on your own discretion.

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.