Introduction to Quantum Mechanics · Problem 1.13

The Wave Function — David J. Griffiths

Physics — Quantum Mechanics · numerical_probability

Problem

Check your results in Problem 1.11(b) with the following "numerical experiment." The position of the oscillator at time tt is x(t)=Acos⁡(ωt).x(t) = A\cos(\omega t). You might as well take ω=1\omega = 1 (that sets the scale for time) and A=1A = 1 (that sets the scale for length). Make a plot of xx at 10,000 random times, and compare it with ρ(x)\rho(x). Hint: In Mathematica, first define x[t_] := Cos[t] then construct a table of positions: snapshots = Table[x[π\piRandomReal[j]], {j, 10000}] and finally, make a histogram of the data: Histogram[snapshots, 100, PDF, PlotRange →\to {0,2}] Meanwhile, make a plot of the density function, ρ(x)\rho(x), and, using Show, superimpose the two.

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