I am a noob in Mathematica. I am trying to solve a Quantum Mechanical problem of particle in a one-dimensional box. The program was written for Mathematica 6. But, I ran it in Mathematica 14. The expected output in second to fifth output was like below:
Out[45]= 14.0353 Out[46]= 55.7956 Out[47]= 124.253 Out[48]= 217.721 Out[49]= 333.898
But instead, it shows this:
Out[45]= -4621.58 Out[46]= -1231.51 Out[47]= -869.209 Out[48]= -504.838 Out[49]= -385.284
See below.
What could be causing this? And how to solve the issue?
How to run programs written for Mathematica 6 in Mathematica 14? Some programs show a different output than expected in Mathematica 14. For example, look at the attached notebook
The program gives this output below the matrix in Mathematica 6:
14.0353 55.7956 124.253 217.721 333.898 14.0642 56.2568 126.578 225.027 351.605
But in Mathematica 14, the ouput below the matrix is:
-4621.58 -1231.51 -869.209 -504.838 -385.284 14.0642 56.2568 126.578 225.027 351.605
How can I get the same output as Mathematica 6 in Mathematica 14? What settings should I change? Is there any compatibility setting available?
The equation Det[A] == 0 is of degree 19 with inexact coefficients. Maybe it is a numerical instability issue. If I try
Det[A] == 0
HornerForm[Det[A]] /. Solve[Det[A] == 0]
in version 14 I get numbers as high as -473. What happens in version 6?
-473
Turns out the issue is a version issue. The program shows a different output in Mathematica 14 than in Mathematica 6. How to solve this?
Here is a way:
{E1, E2, E3, E4, E5} = X/(16/10*10^-22) /. B[[1 ;; 5]]; TableForm[{{E1, E2, E3, E4, E5}, {E1, E2, E3, E4, E5} // N, {E1ext, E3exact, E4exact, E5exact}} // Transpose, TableHeadings -> {None, {"E symbolic", "E numeric", "Exact"}}]
I would do as much of the calculation in exact arithmetic as possible:
a = 20*10^-9; h = a/20; m = Rationalize[0.067*9.1]*10^-31; hcutsq = ((Rationalize[6.626]*10^-34)/(2*Pi))^2;
This way the numbers turn out quite different. I have no idea if they are still weird.
