down the Laplace equation in spherical
separation of variables to find the equation that will generate the
angular dependence. (You may assume that there is no f-dependence
in order to simplify the mathematics.)
that this is equivalent to Legendre’s equation by letting
two vectors in a plane .
these vectors using the matrix formulation (show work) by rotating them
in the plane through and angle to find the new vectors .
that the dot product doesn’t change
two vectors in 4-space
a Lorentz transformation to find the new vectors in the boosted
coordinate system. Show your work using matrix mathematics (column
vectors, row vectors and 4x4 matrices)
that the inner product
class we developed a matrix operator
Which could be
used to produce a rotation through the angle for the case of a two
component object. How would I extend this so as to rotate a 3-d vector.