## Quantum Mechanics...

Suppose that the Hamiltonian is invariant under time reversal:

[H,T] = 0.

Show that, nevertheless, an eigenvalue of T is not a conserved quantity.

v/r,

## plotting a 2xN matrix...

1. How do I take a 2xN matrix and plot it on a 2D graph by its columns?

2.How do I take a number n and a 2xN matrix and return the product of A^n with the 2xN matrix, where A is a 2x2 matrix?

3.How do I, using your two functions above, write a procedure which plots on the same graph the result of multiplying the 2xN matrix by A^n for n = 0,1,2..10. How do i cause these sequence of plots to be displayed as an animation?

## define_external : importing a Fortran subroutine p...

Hi,

I'm working on a computational physics project and prefer to use Fortran codes (compiled by MVS-9) with Maple power together.

In recent days I've changed some compiler options in MVS and unfortunatly (I don't remember the options) nothing works well as before.

For example, as I try to use a simple code like this:

## Welcome to How do I...with MapleSim...

This forum is the place for you to post all of your MapleSim questions.

## 3-D system: how many solutions?...

Hi there,

So my problem is to find the solution(s) of a 3-D system. I can get Maple to spit out a solution (at times), but I am looking for reassurance that this is indeed the solution (if unique, and if not what the other solutions may be). Increasing Digits makes Maple "lose" the solution and return a blank-- normal behavior? Looking at the 3-D plot of the system offers something to puzzle over.

I set up the system in  (x,c,q):

xd := x^.5-.1*x-c;
cd := (.5/x^.5-.1-q)*c;
qd := -(q-.2e-1)*(q-.3e-1)+(q-.25e-1)*(.5/x^.5-.1-q)*c/(x^.5-.1*x-c);

I look for a solution with fsolve:

Digits:=10: interface(displayprecision=10):
ss:= fsolve({xd,cd/c,qd}, {x,c,q}, avoid={x=0, c=0, q=0});
xs:=subs(ss,x): cs:=subs(ss,c): qs:=subs(ss,q):

Maple gives:

ss := {c = 2.399289639, q = .2511089584e-1, x = 15.97164840}

If I raise digits to 15, Maple can't solve it anymore. Perhaps this is normal behavior.

I'd like some reassurance that this solution is indeed a solution. Simply feeding the fsolve output back into the system will not work because of a division by zero:

eval(xd,{x=xs,c=cs,q=qs}); eval(cd,{x=xs,c=cs,q=qs}); eval(qd,{x=xs,c=cs,q=qs});

yields:

0.
-.9597158556e-10
Float(-infinity)

I decided to look at the 3-D plot. The plot of the system suggests that there may be several solutions.

The plot:

px:=implicitplot3d({xd}, x=0..25,c=0..5,q=0.02..0.05, numpoints=10000, plotopts, colour=brown): pc:=implicitplot3d({cd/c}, x=0..25,c=0..5,q=0.02..0.05, numpoints=10000, plotopts, colour=green):
pq:=implicitplot3d({qd}, x=0..25,c=0..5,q=0.02..0.05, numpoints=10000, plotopts, colour=blue):
display3d({pq}, orientation=[-25,70]);
display3d({px,pc,pq}, orientation=[95,90], projection=1);

The plot is not very clean, and no matter how hard I've tried, by turning it around and zooming near the Maple solution, it is not clear that there are no other solutions. (well perhaps it is clear from the equations themselves, but I couldn't work it out and resorted to the numerical approach)

## Rioboo's algorithm for real rational functions?...

```Does somebody have a sheet covering that algorithm for continous
anti-derivatives of rational functions (Bronstein's book §2.8
"Integration of transcendental functions")?

Or can show me, how to extract it from Maple's library in case
it is there (and I guess Maple covers that ...) for explicite
use?
```

## Partial Fractions Finder...

This is a unique, powerful and useful tool that will help students do decompositions of rational functions. See the attached worksheet. Also, you can view an interactive video tutorial that shows you how to use the Partial Fractions Finder: (Ctrl + click on link below) Video Tutorial: Partial Fractions Finder

## Write a procedure...

Write a procedure

input:a polygon and a linear transformation

output :applying the transformation to the polygon

Find the coordinates of the linear transformation that would have  the a larger square to the pink (smaller) square.Apply the transformation to the blue square.

I have tried the Physics package. First of all, how can I define a non-ortogonal basis (using kets)? Suppose I have a basis formed by linearly independt vectors. How to set them non-ortogonal?

## Optimal control problem...

Hello! Sorry for my bad english. I have question: How do I solve non-linear otimal control problem in Maple (my version of program is 11)? I interesting in numeric result, non symbolyc. Standart tools didn't solve my problem. Please give my link for maple worksheets or other information on this topic. Thank you!

## Dyadics and indeterminte vector products...

How does one do the indeterminate vector product with and Dyadic calculus operations with Maple 12?

## Problems with Physics package...

I just upgraded to Maple 12 because of its ability to perform abstract index calculations. However, I'm having trouble getting started with it. My first problem is with the Simplify command: if I define a completely symmetric tensor using the command

Define(T,symmetric);

and an antisymmetric tensor using the command

Define(w,antisymmetric);

then

Simplify(T[mu,nu,rho]*w[mu,nu]);

correctly returns 0. However, if I define T to be symmetric in only its first two indices,

Define(T[mu,nu,rho],symmetric={mu,nu});

## Atkinson T statistic...

Could guide me where to find information on the Atkinson T statistic in linear regression.

Best regards

## Level Curves and Cross Sections...

See the interactive Level Curves and Cross Sections video tutorial: (Ctrl+click on link) Video Tutorial: Level Curves and Cross Sections   Alternatively, you can view a worksheet that provides a review and an example of level curves and cross sections.