Thanks for the response, kcrisman. The questions you ask are exactly
what I've
been pondering myself.
After much additional messing around, I found the problem (and its
solution):
the factor in front should be 2/a, not a/2:
sage: var('a, n, x')
(a, n, x)
sage: assume(a>0)
sage: assume(n,'integer')
sage: integral(2/a * x * sin(n*pi*x/a)^2,x,0,a).simplify_full()
1/2*a
(I apologize for taking up bandwidth on this.)
Jim
On Oct 19, 2009, at 12:25 AM, kcrisman wrote:
> On Oct 19, 1:02 am, Jim Clark <jimfortheea...@earthlink.net> wrote:
>> Hi sage supporters,
>>
>> I am attempting to verify some properties of the quantum mechanics
>> "particle in a box" problem.
>> integral() is returning the wrong results for <x> and <x^2>.
>> I can't figure out what I might be doing wrong.
>>
>> To find <x>:
>> ---------------------------------------------------------------------
>> -
>> | Sage Version 4.1.2, Release Date:
>> 2009-10-14 |
>> | Type notebook() for the GUI, and license() for
>> information. |
>> ---------------------------------------------------------------------
>> -
>> sage: var('a, n, x')
>> (a, n, x)
>> sage: assume(a > 0)
>> sage: assume(n, 'integer')
>> sage: integral(a/2 * x * sin(n*pi*x/a)^2,x,0,a).simplify_full()
>> 1/8*a^3
>>
>> The result should be a/2, which can almost be verified by inspection,
>> but I have worked out the integral by hand also, and I am
>> confident that
>> a/2 is the correct result.
>
> Dear Jim,
>
> Hmm, I get the same answer as Sage with Wolfram Alpha. Are you sure
> you typed this in correctly? Don't forget to use u-substitution in
> calculating <x> - it looks like maybe something like that might
> account for the missing constants.
>
>
> Hope we can resolve this for you!
>
> - kcrisman
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to
sage-support-unsubscr...@googlegroups.com
For more options, visit this group at
http://groups.google.com/group/sage-support
URL: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
