Tru Physics

Problem 1.13 – Griffith’s Intro to QM

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Problem 1.13

Check your results in Problem 1.11(b) with the following “numerical experiment.” The position of the oscillator at time t is

x(t) = A \cos(\omega t).

You might as well take \omega = 1 (that sets the scale for time) and A=1 (that sets the scale for length). Make a plot of x at 10,000 random times, and compare it with \rho(x).
Hint: In Mathematica, first define

x[t_] := Cos[t]

then construct a table of positions:

snapshots = Table[x[\piRandomReal[j]], {j, 10000}]

and finally, make a histogram of the data:

Histogram[snapshots, 100, “PDF”, PlotRange -> {0,2}]

Meanwhile, make a plot of the density function, \rho(x), and, using Show, superimpose the two.

Solution:

problem 1.13 griffiths solution
problem 1.13 griffiths solution graph

Problem 1.13 Solution (Download)

Find more Griffith’s solutions here.

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