Eigenvalues of non-commuting objects...

Hi guys,

If I have a Hermitian 4x4 Matrix with elements that behave like complex numbers except that they do NOT commute. Is it possible to diagonalize this Matrix using Maple and the Eigenvectors - method of the LinearAlgebra package?

Cheers

NOh

P.S.: I am using Maple 18

IT Solutions for the Next Generation of Engineers

Maple 18

Presented at the National University of Trujillo - CUICITI 2014.

IT Solutions for the Next Generation of Engineers

Descarga aqui los Slides de la presentación/mw CUICITI-2014

CUICITI_09102014.pdf

Soluciones_Informáticas_para_la_siguiente_generación_de_Ingenieros.mw

Lenin Araujo Castillo

Physics Pure

Computer Science

QM perturbation theory: too many levels of recursi...

Hello everyone,

I've been trying to do some perturbation theory and ran into some problems I don't quite understand. I implemented the Hamiltonian of the Bose-Hubbard model and treated the hopping as a perturbation. Calculating the second order energy shift is easily accomplished, but when I'm only interested in one of the two occuring terms, I run into problems. The calculation takes minutes to finally fail, giving me an "too many levels of recursion"-error. I need to be able to just pick a few terms for some calculations, I'm doing, and can't figure out what I might be doing wrong. Here is the source code (download is below):

 >
 >
 >
 (1)
 >
 >
 (2)
 >
 >

It would be great, if someone could point out the mistake, I'm making. I copy/pasted the last line, so there shouldn't be any typos.

Sören

solving for x gives me x->...

Every time I try to solve for a variable it gives me an arrow.

ex solve(5.6*10^-4=((x)(x))/(0.2-x),x)

gives me

x -> 7/62500 - 7/12500 x

How do I get it to stop giving me the x -> ?

Or at least reset some options so I don't have to reinstall the whole thing?

How to calculate eigenvalues of complex symbolic M...

Hello,

first of all, this is my very fist question in this forum, so please excuse some formal mistakes I may make...

Using Maple 18.01 on Windows 7 64bit

To the topic: I want to calculate the eigenvalues of a complex matrix like this (just as an example):

M := Matrix(2, 2, {(1, 1) = a+2.5*I, (1, 2) = 1-I*a, (2, 1) = 4, (2, 2) = a})

When I try to calculate

Eigenvalues(M)

I get

Error, (in LinearAlgebra:-Eigenvalues) expecting either Matrices of rationals, rational functions, radical functions, algebraic numbers, or algebraic functions, or Matrices of complex(numeric) values

Strange, because if I replace the "2.5" with just "2", so an integer instead of a float, I get results:

I don't understand this strange behavior, since Mathematica i.e. calculates everything just fine...:

Thanks in advance for any suggestions.

How to tell Maple that |a,b,c> is an eigenvector o...

Hi everyone,

I am exploring the physics package a bit. However, in the documentation I didn't find anything about how to setup operator-ket relations like:

A | l,m,n > = f(l,m,n) | g(l,m,n), h(l,m,n), z(l,m,n) >

The Creation and Annihilation operators were the only predefined ones I found.

Cheers

NOh

help. How do you enter limits, is there a lim as x...

My instructor gave me the problem lim as x goes to 0 of ((2 + x)^3 +8)/x I can't figure out how to get the lim as x goes to, to show up.  There is no button for it in the expressions pallette like there is for things like the piecewise function. My instructor won't help me.  Is there a basic guide I can buy or something.  This software isn't very intuitive.

How to get maple 18 working?...

The installation / activation went without trouble. The problem occurs when I want to start Maple. The splash screen shows up with a blue loading bar and that's it. It just keeps loading, sometimes it gets to the end but nothing more. Taskmanager shows a CPU usage of +/- 15%. I searched the net for answers but I only found two similar situations. One was due to the java heap size and another one due to tcp/ip problems. I checked both but the problem still persists. I really need Maple for my courses and you guys are my last resort. I'm running it on win7 64bit and I tried both 32 and 64bit Maple.

Dirac Algebra using the Physics Package...

Hi,

I'm trying to set up the dirac algebra using the Physics package in maple 18. There are dirac gamma matricies (Dgamma) already specified, but I can't seem to manipulate their commutation relations.

So I've tried building my own:

restart;
with(Physics);

Setup(noncommutativeprefix = {gamma});

g[1] := gamma[1]; g[2] := gamma[2]; g[3] := gamma[3]; g[4] := gamma[0];

InverseMetric := rhs(g_[`~mu`, `~nu`, matrix])

Algebra :=  (a, b) -> %AntiCommutator(g[a], g[b]) = 2*InverseMetric[a, b];

Rules := Matrix(4, 4, Algebra);

Setup(algebrarules = Rules);

Error, (in Physics:-Setup) unable to set AntiCommutator(gamma[0], gamma[1]) = 0 because, taking into account {AntiCommutator(gamma[0], gamma[0]) = 2}, we would have gamma[0] and gamma[0] anticommutative and AntiCommutator(gamma[0], gamma[0]) <> 0

It seems like Maple can't handle the Dirac Algebra? Or have I done something obviously wrong?

Any help is appreciated.

Thanks

How do I magnify text in menus, palettes, plots et...

Hi,

I use Maple on my laptop computer (windows 8.1) with a small screen. My problem is that the text in the menus, palettes, plots etc. are so small so I can´t read it. I have set Large toolbar icons under the menu tools-options-interface and I use the zoom buttom on the toolbar but this only magnify the text in a document. I also use the magnifying glass in windows, but I find it very inflexible. Is there any better solution to this problem?

Kind Regards

Leif Jonson

Having trouble with Maple evaluating an integral....

Below is the function that I have.

f := (t-1)^(1/3)

p:=2;

b[n] := 2/p*(Int(f*sin(2*Pi*n*t/p), t = 0 .. p))

I also included a picture below to show what it is doing. Some help would be greatly appreciated. All I need to know is why maple doesn't want to evaluate bn?

How to get a procedure to return an output as a {s...

So if I have a procedure like

with(GraphTheory)

tneighbors := proc (G::Graph)

local numvertices::integer, i::integer, currentvertex;

numvertices := nops(Vertices(G));

for i to numvertices do

currentvertex := Vertices(G)[i];

if nops(Neighbors(G, currentvertex)) = 2 then print(currentvertex)

end if;

end do;

end proc;

How do I make it so the output gets returned as a set?

For example, if I do  twoneighbors(G); and get
1

7

4

How do I make it so the output is listed as a set like {1,4,7}? Thanks.

find the domain of a function...

Hi Maple friends.

How can I find the domain of y=sqrt(3*x-5)? or of y=1/(x+2)^2?

When I open my file I got an error message says "there were problems during loading process"

and some of my text are missing.

Maple Worksheet - Error

Can anyone help me,please

problem of numerical integration with method = _d0...

See AAAA.mw

The alpha and beta are 'randomly' chosen, both >0, to produce some values, hence a value for the target function to optimize.

I am having trouble to evaluate the expression in the middle of the calculation.

Sometimes, the 'chosen' alpha and beta works fine with 'method = _d01amc' for numerical integration. and such way is really "fast".

But sometimes, the the 'chosen' alpha and beta will fail. Even when both of them are perfectly defined. and the integral can be easily evaluated using Int() and then evalf().

So what's be best way to proceed?

Thanks,

casperyc

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