rotation operator in a sentence

1. is a 90?anticlockwise rotation operator in 2d.
2. Taylor expanding to first order in " ? " gives the infinitesimal rotation operator:
3. The space of rotations is isomorphic with the set of rotation operators and the set of orthonormal matrices with determinant + 1.
4. The relationship between the angular momentum operator and the rotation operators is the same as the relationship between lie algebras and lie groups in mathematics.
5. Likewise, exponentiating the representations of the generators gives the representations of the boost and rotation operators, under which a particle's spinor field transforms.
6. It's difficult to find rotation operator in a sentence.
7. The relationship between angular momentum operators and rotation operators is the same as the relationship between Lie algebras and Lie groups in mathematics, as discussed further below.
8. Though all three movements can be represented by a rotation operator with constant coefficients in some frame, they cannot be represented by these operators all at the same time.
9. In the case of the free particle, the unitary operator which produces the symmetry is the rotation operator, which rotates the wavefunctions by some angle while otherwise preserving their shape.
10. Exponentiating the generators gives the boost and rotation operators which combine into the general Lorentz transformation, under which the spacetime coordinates transform from one rest frame to another boosted and / or rotating frame.
11. from this and the infinitesimal rotation operator and its Hermitian conjugate, and ignoring second order term in ( \ delta \ theta ) ^ 2, one can derive the commutation relation with the rotation generator:
12. That such a rotation exists corresponds precisely to a main result of the mathematical theory of rotation operators, the ( only real ) eigenvector of the rotation operator corresponding to the desired re-orientation is this axis.
13. That such a rotation exists corresponds precisely to a main result of the mathematical theory of rotation operators, the ( only real ) eigenvector of the rotation operator corresponding to the desired re-orientation is this axis.
14. Given the current orientation of the craft, and the desired orientation of the craft in cartesian coordinates, the required axis of rotation and corresponding rotation angle to achieve the new orientation is determined by computing the eigenvector of the rotation operator.
15. Again, a finite rotation can be made from lots of small rotations, replacing ? " ? " by and taking the limit as " N " tends to infinity gives the rotation operator for a finite rotation.
16. Because this is the matrix of the rotation operator relative the base vector system \ hat { a } \, \ \ hat { b } \, \ \ hat { c } the eigenvalue can be determined with the algorithm described in " Rotation operator ( vector space ) ".
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