Problem 1.13 | Griffiths' Introduction to Quantum Mechanics | 3rd Edition
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Загружено: 2024-03-27
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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[$\pi$RandomReal[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.
https://tru-physics.org/2023/05/24/pr...
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