Chemical Solution Wizard vs Quantum Wave in a Box

Chemical Solution Wizard has been designed to help with preparation and parameterization of complex chemical solutions and derivation of molar weight from chemical formula. Numerous parameters of the complex mixture, such as molarity, molality, mg/ml, solute moles, total volume etc. can be calculated based upon initial data provided, such as: initial molar concentrations of the starting solutions, initial volumes, desired molar ratios and additional solvent volume (dilution). This application targets two main solution preparation tasks: First, "Mixture of Solutions", makes it easy to parameterize complex mixture of several initially provided solutions. And second, "Dissolution", deals with solution formed by dissolution of solid solutes. Layout of "Mixing solutions". Each row represents initial solution, which is going to be mixed to produce a final complex solution. The initial solution parameters to start with are: solute’s molar weight (optional), solute’s molar concentration and volume of the initial solution. Last cell represents molar fraction of the particular solute in the final solution that will be calculated automatically or may be adjusted later on to get the desired components ratio. Bottom row represents final solution parameters: volume of pure solvent that optionally can be added to dilute the solution, Total Molarity and Total solution volume, that can be adjusted at any time, on condition that molar concentrations of the initial solution/s are provided. Layout of "Dissolution". Similarly, each row represents different compound (solid this time) that will be dissolved in the known final volume of the resulting solution. “Solute moles” are the output only cells that will be filled automatically. Final solution parameters row is comprised of absolutely required final solution volume cell and optional final density cell, which may come in handy for calculation of molality. Application features: Unlimited number of components is available. Additional components are added by touching “Solution (+)” field and deleted by touching the top right title field signed with (-). The components list is numbered and scrollable. The application is fully interactive: all parameters are updated instantly after any input that confirmed by pressing "Done" button in the keyboard! (if data is sufficient, otherwise warning will be shown). CSW is now includes molar weight analyser. Pressing of the arrow button in Mw field derives the molar weight of molecular formula in the name field. Examples of supported molecular formula styles: MnSO4.H2O, MnSO4*H2O, (NH4)2CrO4, (NH4)2Fe(SO4)2.6H2O, Ba(C2H3O2)2. In “Mixture”, if molecular weights (Mw, units "g/mole") of solutes are provided as well, then concentrations in units of grams of solute per litre of solution ("g/l" equivalent to "mg/ml") will be calculated. In "Dissolution", long press on Total Molarity title field will call the menu, where user can choose the options for solution parameters adjustment upon change in total molarity. Please check the molar ratios to ensure that all starting components are included! The application will expel components for which insufficient data is provided! Thus, for example concentration in mg/ml cannot be calculated if Mw of solute is not provided. Similarly, Molality cannot be calculated if final solution density is missing. If user updates molar ratios (percents only), application will not start the calculation until sum of the ratios will be 100 exactly and obviously, not before than initial concentrations (in "Mixing solutions") or Mw (in "Dissolution") are provided. Total Concentration in "mg/ml", Total Moles and Molality fields are for output only. Please confirm input by pressing "Done" or "Enter" button in the keyboard to let application know that data is ready. Application is not sensitive for an unconfirmed input for a good reason. Application assigns dot as a decimal separator.

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.