- #1
bryanso
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- Homework Statement
- In Associated Legendre Function with Angles ... why is the following argument used?
- Relevant Equations
- ## \sqrt{1 - x^2} = sin\,\theta ##
In Wikipedia https://en.m.wikipedia.org/wiki/Associated_Legendre_polynomials, Section Reparameterization in terms of angles, I see this argument:
Let ## x = cos\,\theta ##
## \sqrt{1 - x^2} = sin\,\theta ##
This is also in Griffiths' Introduction to Quantum Mechanics.
Why is this a valid argument?
The LHS is always positive. The RHS is sometimes positive and sometimes negative. ##\theta = -1## makes it wrong.
Let ## x = cos\,\theta ##
## \sqrt{1 - x^2} = sin\,\theta ##
This is also in Griffiths' Introduction to Quantum Mechanics.
Why is this a valid argument?
The LHS is always positive. The RHS is sometimes positive and sometimes negative. ##\theta = -1## makes it wrong.
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