1
$\begingroup$

The expression $\sqrt{L^2 M+\sqrt{L^2 (-J^2 + L^2 M^2)}}/\sqrt{2}$，can be simplified into $\sqrt{L}(\sqrt{LM + J}+\sqrt{LM - J})/2$, but how can I obtain this result with Mathematica?

That is, how can I simplify

Sqrt[L^2 M + Sqrt[L^2 (-J^2 + L^2 M^2)]]/Sqrt[2]

into

Sqrt[L]/2 (Sqrt[L M + J] + Sqrt[L M - J])
Improve this question
$\endgroup$
5
  • $\begingroup$ Have You tried Simplify? $\endgroup$
    – Wojciech
    Nov 13, 2013 at 9:34
  • $\begingroup$ Please correct your expressions clarify the layout. Note: LM is not equivalent to L M. $\endgroup$
    – Yves Klett
    Nov 13, 2013 at 10:13
  • $\begingroup$ sometimes the best you can do is get mathematica verify that your expression is the same, have you done that? Show that code... $\endgroup$
    – george2079
    Nov 13, 2013 at 13:11
  • $\begingroup$ Equal[{Sqrt[L^2 M + Sqrt[L^2 (-J^2 + L^2 M^2)]]/Sqrt[2], Sqrt[L]/2 (Sqrt[L M + J] + Sqrt[L M - J])}] returns true, but I'm not sure what are we trying to achieve - to verify the statement or to get Mathematica to return the simplified form? $\endgroup$
    – Wojciech
    Nov 13, 2013 at 13:23
  • $\begingroup$ @WojciechSitkiewicz that is incorrect syntax for equal. The expressions are in fact only equal under certain conditions (eq J=1,M=1,L=-1) they are not equal. $\endgroup$
    – george2079
    Nov 13, 2013 at 14:56

2 Answers 2

Reset to default
1
$\begingroup$

Are you sure that the first expression can be simplified to the second?

o1 = Sqrt[L^2 M + Sqrt[L^2 (-J^2 + L^2 M^2)]]/Sqrt[2];
o2 = Sqrt[L]/2 (Sqrt[L M + J] + Sqrt[L M - J]);

and

ru = {L -> 5, M -> 2, J -> 3.};

Then just

o1 /. ru
o2 /. ru
Improve this answer
$\endgroup$
2
  • $\begingroup$ Sorry, it is " plus " in the first equation. $\endgroup$
    – user10537
    Nov 13, 2013 at 9:43
  • 2
    $\begingroup$ Given that the equation was incorrect I suggest you delete your answer, as it actually doesn't answer the question. $\endgroup$
    – Sjoerd C. de Vries
    Nov 13, 2013 at 13:12
1
$\begingroup$

By squaring both expressions and making some assumptions we can show them equal..

     Simplify[
            (Sqrt[L^2 M + Sqrt[L^2 (-J^2 + L^2 M^2)]]/Sqrt[2] )^2 
              ==
            ( Sqrt[L]/2 (Sqrt[L M + J] + Sqrt[L M - J]))^2  , 
       Assumptions -> { L > 0, M > Abs[J/L]}] 

     (* True *)

As near as I can tell under those assumptions this equality should still hold without squaring the expressions, but Simplify fails to see that for some reason.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.