AP Physics 2 full-length practice tests, diagnostic exams, andflashcards

Handbook of Engineering Physics with diagrams, learn a topic in aminute

An education app that covers the most vital concepts of physics.

Probably the best Physics Notes for students and teachers, download& share It.

Physics 2 Go! Part 1 - InteractiveQuantumMechanicThe app calculates the basic formula of quantum mechanics,theone-dimensional Schrödinger equation for a set ofpredefinedpotentials or a self-defined potential.The main page contains fields/lists for:defining the size of the box of the system by setting x_minandx_maxsetting the step size delta t used in the time evolution,smallervalues usually give more accurate resultspicking a potential. By choosing "user defined" you can writeyourown expression in the field "potential" (like, e.g., x^2).The parser for the expression is relatively simple andhopefullynot too buggy. It uses "x" as variable, "+-*/^", brackets"()" andthe functions sin,cos,tan,exp,log,step (step(x)=1 forx>=0,otherwise 0), and abs (absolute value).You can plot the wave function by pressing "Plot It!". Theplotshows real (blue) and  imaginary (red) part of thewavefunction, the right y axis labels the  values for thewavefunctions. The  potential is plotted in black(valuescorrespond to the labels of the left y axis). The whitelinedepicts the energy of the state. Tapping "Stop" will interruptthecalculation.Following additional controls exist:With "width" and "position" you can define the width and positionofthe initial Gaussian wavefunction. By pressing "Init WF" thewavefunction is initialized.Choosing "rea"' or "imaginary" time you can pick the evolutionofthe wave function in real or imaginary time. For the choiceofimaginary time the solution will relax to the static groundstate.Using real time you see the oscillation of the wave functionwithtime. However, due to the numerics there might be effectivelyasmall imaginary part, which drives the system to theoscillatingground state after a while. The stability of thereal-timebehaviour can depend on the size of the chosen time step.Note thatespecially for narrow potentials the real-time solutioncan becomeunstable (and obviously incorrect) at this stage of theappdevelopment.You can plot the "ground state" or first "excited state".Whenpicking the excited state, the ground state calculation willstopand the functions will change colors to orange and purple.Theexcited state will be orthogonal to the ground state. Therefore,ifthe ground state has not yet reached its stable value, alsotheexcited state won't be correct.Enjoy the app!

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