Question

I’m currently doing some normalization along the lines of:

J = Integrate[Psi[x, 0]^2, {x, 0, a}]
sol = Solve[J == 1, A]
A /. sol

For this type of normalization, the negative square root is extraneous. The result of this calculation is:

In[49]:= J = Integrate[Psi[x, 0]^2, {x, 0, a}]
Out[49]= 2 A^2

In[68]:= sol = Solve[J == 1, A]
Out[68]= {{A -> -(1/Sqrt[2])}, {A -> 1/Sqrt[2]}}

Even if I try giving it an Assuming[…] or Simplify[…], it still gives me the same results:

In[69]:= sol =  Assuming[A > 0, Solve[J == 1, A]]
Out[69]= {{A -> -(1/Sqrt[2])}, {A -> 1/Sqrt[2]}}

In[70]:= sol =  FullSimplify[Solve[J == 1, A], A > 0]
Out[70]= {{A -> -(1/Sqrt[2])}, {A -> 1/Sqrt[2]}}

Can anyone tell me what I’m doing wrong here?

I’m running Mathematica 7 on Windows 7 64-bit.

Answer 1

Solve doesn’t work like this. You might try Reduce, instead, e.g.

In[1]:= Reduce[{x^2 == 1, x > 0}, x]
Out[1]= x == 1

It’s then a little tricky to transform this output to replacement rules, at least in the general case, because Reduce might use arbitrary many logical connectives. In this case, we could just hack:

In[2]:= Solve[Reduce[{x^2 == 1, x > 0}, x], x]
Out[2]= {{x->1}}