Physics 2 Go Part 1

Do Quantum Mechanics With Your Phone!

Physics 2 Go! Part 1 - Interactive Quantum Mechanic

The app calculates the basic formula of quantum mechanics, the one-dimensional Schrödinger equation for a set of predefined potentials or a self-defined potential.

The main page contains fields/lists for:

defining the size of the box of the system by setting x_min and x_max

setting the step size delta t used in the time evolution, smaller values usually give more accurate results

picking a potential. By choosing "user defined" you can write your own expression in the field "potential" (like, e.g., x^2).

The parser for the expression is relatively simple and hopefully not too buggy. It uses "x" as variable, "+-*/^", brackets "()" and the functions sin,cos,tan,exp,log,step (step(x)=1 for x>=0, otherwise 0), and abs (absolute value).

You can plot the wave function by pressing "Plot It!". The plot shows real (blue) and  imaginary (red) part of the wave function, the right y axis labels the  values for the wave functions. The  potential is plotted in black (values correspond to the labels of the left y axis). The white line depicts the energy of the state. Tapping "Stop" will interrupt the calculation.

Following additional controls exist:

With "width" and "position" you can define the width and position of the initial Gaussian wavefunction. By pressing "Init WF" the wave function is initialized.

Choosing "rea"' or "imaginary" time you can pick the evolution of the wave function in real or imaginary time. For the choice of imaginary time the solution will relax to the static ground state. Using real time you see the oscillation of the wave function with time. However, due to the numerics there might be effectively a small imaginary part, which drives the system to the oscillating ground state after a while. The stability of the real-time behaviour can depend on the size of the chosen time step. Note that especially for narrow potentials the real-time solution can become unstable (and obviously incorrect) at this stage of the app development.

You can plot the "ground state" or first "excited state". When picking the excited state, the ground state calculation will stop and the functions will change colors to orange and purple. The excited state will be orthogonal to the ground state. Therefore, if the ground state has not yet reached its stable value, also the excited state won't be correct.

Enjoy the app!