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Jul
8
comment Defining the Moyal Product in Mathematica
@Karan I think if what you really want is for the star product to keep its defining properties, then either your limiting approach in the earlier comment or brute-force ignoring of the conditional expression should be permitted. The last update to my answer should also do the trick.
Jul
8
revised Defining the Moyal Product in Mathematica
Deal with pathological cases
Jul
8
comment Defining the Moyal Product in Mathematica
@Karan OK - ConditionalExpressions are of course also a warning for you to stop and think about the validity of what you're doing... basically the order of integrations seems to matter, and boundary terms could be cropping up in partial integrations. I think that goes beyond what the question asked for. But I could post a brute-force fix for this issue anyway.
Jul
8
revised Defining the Moyal Product in Mathematica
Omitted discussion of possible bug because it may not be one. Added reference.
Jul
8
comment Defining the Moyal Product in Mathematica
@Karan Yes, I think you're right - I checked again and 9.0.1 isn't working for the star[1/x^2,p] case because it can't do the FT. But in any case, that's a very pathological kind of function, so I'm not totally sure it's a real bug. Are you perhaps doing something in polar coordinates? Then the phase space integral has to be done differently, including the proper Jacobian. So the naive star product definition may not be what you need anyway.
Jul
8
comment Using NDSolve to solve Equation of Motion in cylindrical coordinates
If you're not sure what the correct expression for the canonically conjugate momentum is, write down the Lagrangian in Cartesian coordinates, make the coordinate transformation, and then obtain the momentum from $p_r \equiv \partial{L}/\partial{\dot r}$.
Jul
8
comment Defining the Moyal Product in Mathematica
@RahulNarain Oh, I didn't even notice that the definition of the star product in the question is wrong. The textbook definition is the exponential I wrote down. If you believe my version (which you can find in the literature), then the definition in the question is missing a factor 1/n! under the sum. Also, I of course set h=1. So the discrepancy won't show up unless higher terms n>1 are involved in the sum. I can add some references, but I haven't heard from the OP at all so I don't know if it's worth it. Thanks for checking!
Jul
8
comment Defining the Moyal Product in Mathematica
@RahulNarain The code by belisarius was an example, not intended to be the exact result. He only added up the first 10 terms of an infinite sum, in order to show that the problem lies in the limit of infinitely many terms. So you cannot do my last example with the code in the question or in the comment.
Jul
8
revised Defining the Moyal Product in Mathematica
Addressed possible bug
Jul
8
comment Defining the Moyal Product in Mathematica
@Karan Indeed, I checked and your observation is a bug in Mathematica version 9.0.0 which has been fixed in version 9.0.1.
Jul
8
revised Using NDSolve to solve Equation of Motion in cylindrical coordinates
Discussed angle jump
Jul
8
comment Using NDSolve to solve Equation of Motion in cylindrical coordinates
@acl Good idea. I'll do it soon...
Jul
7
comment Defining the Moyal Product in Mathematica
@Karan must be a problem with version 9. In v. 8 this doesn't happen...
Jul
7
comment Defining the Moyal Product in Mathematica
I can't reproduce this (what version of MMA are you using?). Setting $Assumptions={x>0} before doing the tests, both orders of the star work fine and give consistent results, no left-over FT or deltas.
Jul
7
revised Using NDSolve to solve Equation of Motion in cylindrical coordinates
Discussed consistency
Jul
7
answered Using NDSolve to solve Equation of Motion in cylindrical coordinates
Jul
7
reviewed Close Creating a Network from a Output
Jul
7
reviewed Close Why does pattern test not work in this case to restrict the function parameters?
Jul
6
comment How to use multiple pure functions correctly?
Yes, that's all possible, but it's very hard to read - perhaps more difficult to read than it is to write it... And (#&) is basically just shorthand for Function anyway.
Jul
6
answered How to use multiple pure functions correctly?