WWW location: http://www.fi.uib.no/AMOS/matlab/AllDirac.html
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New today (Oct.2. 95)
Text of
NORDIC MATLAB CONFERENCE contribution, postscript
(contact: ladi@sparc-atom.fi.uib.no )
Further development of our research applications ideas resulted in a small package suitable for teaching quantum mechanics, based on the idea of an interpreter written using Matlab's language.
The interpreter can be easily extended and adapted to other problems, for example to define vectors with vectors as elements (indexed vectors) or multidimensional arrays. Here is a short example of a dialog
Dirac : |a>
Matlab: --> a
a =
1
0
Dirac : |b>
Matlab: --> b
b =
0
1
Dirac : < a | b >
Matlab: --> (a)'*b
ans =
0
Dirac : D: [X] %% Declare, not fully exploited yet.....
DECLARED =
|a> |b> |c> |d> (c1) (c2) [O1] [O2] [U]
[sig2] [sig2] [u1] [u3] [X]
Dirac : M: X=[0.2 0.5; 0.5 0.2]; %% Use matlab notation
Dirac : X
Matlab: --> X
X =
0.2000 0.5000
0.5000 0.2000
Dirac : < a | X | b>
Matlab: --> (a)'*X*b
ans =
0.5000
Projection operators are are often a difficult topic. In Dirac notation,
using
using P = | b > < b |
------------------------
Dirac : | b > < b |
Matlab: --> b*(b)'
ans =
0 0
0 1
We can e.g. easily demonstrate
that P . P = P
------------------
Dirac : ( | b > < b | )( | b > < b | )
Matlab: --> (b*(b)')*(b*(b)')
ans =
0 0
0 1
Dirac : | b > < b| b > < b |
Matlab: --> b*(b)'*b*(b)'
ans =
0 0
0 1
with original nonorthogonal vectors |a> |b> |c>
(normalize them by |b> = |b>/ sqrt(< b | b > ) etc... )
we construct orthonormal |u> |v> |w>
|u> = |a>
|v> = ( U - | u > < u | ) |b> and normalize as above
|w> = ( U - | u > < u | - | v > < v | ) |c> and normalize ....
where U is an appropriate unit matrix
just a little note: using matlab over large distance: use terminal tek401x (remember to start without DISPLAY set) saves time !