Three spin-1/2 particles are fixed in position on the vertices of an equilateral triangle. the interaction amongst themselves and with a uniform external magnetic field, b, is described by the hamiltonian where s, i 1,3, are spin operators, and a is a constant (in units of energy/12). (a) obtain the eigenvalues and eigenvectors of h (b) discuss the degeneracies of the spectrum when b-0. (c) discuss the nature of the ground state when a 0 and when a < 0, still for b 0. (d) discuss the effect the magnetic field causes to the degeneracies when it is switched on.

Your 249 ml cup of coffee is too hot to drink when served at 82 degree celsius. what is the mass of an ice cube taken from a -21 degree celsius freezer, that will cool your coffee to a pleasant 54 degree celsius. specific heat of the water is 4190 j/kg c, specific heat of ice is 2090 j/kg c, heat of fusion of ice is 3.33 x 10^5 j/kg

This problem has been solved! see the answera non-uniform fire escape ladder is 6.0m long whenextended to the icy alley below. it is held at the top by africtionless pivot, and there is neglibible frictional force fromthe icy surface at the bottom. the ladder weighs 250n, and it'scenter of gravity is 2.0m along the ladder from the bottom. amother and child of total weight 750n are on the ladder 1.5m fromthe pivot. the ladder makes an angle θ with the horizontal.find the magnitude and direction ofa) the force exerted by the icy alley on the ladderb) the force exerted by the ladder on the pivotc) do your answers in part a and b depend on the angle?

The frequency of the fundamental of the guitar string is 320 hz. at what speed v do waves move along that string?