How can I derive the root diagram of the SU(2) group by using the Pauli Matrices?

thanks,

dc

A string with a lead ball of mass m is slowly pulled upward through a small hole. Consider the work done on the system during this process. Find the change in energy and the frequency of this pendulum during this "adiabatic process", assuming the amplitude of the pendulum to be small.

Sorry I don't have a picture.

(Imagine the situation of the wire holding the chandalier in your home being slowly pulled up through a small hole through the roof while it is slowly oscillating in one dimension, or in a single plane.)

A problem instructed me to construct a Taylor/Maclaurin series for cot(x) by dividing cos(x) by sin(x).

I did this quotient by putting both summations over each other then cancelling common terms.

I've always had some difficulties with summation, or the rules of the summation symbol and would like to know if that operation was legal.

In this case both summations began from the same starting point for the dummy variable, n.

Whenever this is the case is it correct to say that the quotient of two sums is the sum of the quotient?

very respectfully,

I'm trying to orthonormalize the set of basis vectors of the form form p(x)*exp(-x^2/2), where p(x) is a polynomial of degree less than N.

The basis I'm using for this function space is |e1> = exp(-x^2/2), |e2> = x*exp(-x^2/2), |e3> = x^2 * exp(-x^2/2), and so on.

However the GramSchmidt procedure in the LinearAlgebra package only accepts vectors.

Can someone help me to get around this, and use some procedure to orthonormalize the first four bases for this function space?

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Can someone help me evaluate the last integral?

thanks,

v/r,