Solve doesn't give me all the solutions I expect

Question

I have a problem with Mathematica 10, and I really don't know what's happening here. I try to plot some orbitals and then solve a simple equation. But Nathematica only gives me one the solution, phi -> -Pi/2, instead of two which I think should be there. Also it doesn't tell me, what theta should be.

When a friend of mine, who still uses Mathematica 9 runs the exact same code, he gets the right result. Why?

Clear[Y11, Y112, ph, th];
Y11 = SphericalHarmonicY[1, 1, th, ph];
Y112 = SphericalHarmonicY[1, -1, th, ph];
Fx = 1/Sqrt[2]*(Y11 - Y112);
Fy = 1/Sqrt[2]*(Y11 + Y112);
Solve[Abs[Fx]^2 == 0]

I also tried to use reduce command or to write

Solve[Abs[Fx]^2 == 0, {ph, th}]

but this doesn't work as well.

P.S.: The first picture shows my friend's code and the second one mine.

It is not surprising at all, I am not sure you can get more solutions with Reduce, but certain clever approach could. You should remember limitations of Solve, e.g. I recommend to read e.g. What is the difference between Reduce and Solve?. — Artes, Dec 05 '15 at 18:52
Edit your question and Copy and Paste the code into the question so that others can run it and offer you help. Format the code when you paste it with the code button. — Edmund, Dec 05 '15 at 18:52

bbgodfrey · Accepted Answer · 2015-12-06T02:09:09.103

5

Taking Abs and squaring a quantity equal to 0 adds nothing and apparently confuses Reduce. Try

Reduce[Fx == 0, {ph, th}] // Simplify
(* C[1] ∈ Integers && (th == 2 π C[1] || π + 2 π C[1] == th || ph == π (1/2 + C[1]))*)

edited Dec 06 '15 at 02:09

answered Dec 05 '15 at 20:31

bbgodfrey

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Solve doesn't give me all the solutions I expect

1 Answers1