Getting Wrong Numbers in Output for a Quantum Mechanics problem

Questions
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1

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.

Open in Wolfram Cloud ↗

What could be causing this? And how to solve the issue?

2

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.

3

Sorry, there was a mistake in the question. The expected output in second to fifth output is 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
4

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,
   {E1exact, E2exact, E3exact, E4exact, E5exact}} //
  Transpose,
 TableHeadings -> {None, 
   {"E symbolic", "E numeric", "Exact"}}]
5

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?

6

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?

2024-02-21T00_32_45Particle in a Box.nb (15 KB)

7

The equation Det[A] == 0 is of degree 19 with inexact coefficients. Maybe it is a numerical instability issue. If I try

HornerForm[Det[A]] /. Solve[Det[A] == 0]

in version 14 I get numbers as high as -473. What happens in version 6?