F.1 Josephson

(b) The commutator relation should be
    [delta phi, delta N] = (y/i) m \delta N^{m-1}.
That is, the factor (m-1) outside should have been m, and the relation is
in terms of delta N, not N. Also, you only need to show this for
positive integers $m$.

(c) Changed font of H to make it consistent with the Hamiltonians in 
other sections. Added hint: How is the voltage related to the Hamiltonian?
Added clarification: dN = 1 Cooper pair can be viewed as infinitesimal
change.

(d) Changed request for delta phi approx 1 to <delta phi^2> = 1, to make
it more specific.


F.2 ODLRO

(a) I now clarify that the state we are calculating the reduced density
matrix for is a normalized product of single-particle states, and
that it is a pure state. I also explicitly ask that the formula
be simplified until there are no more integrals.

I've made it more clear that our ket |Psi_N> is a state, that can be
analyzed using the commutation relations -- using the number representation
rather than a position representation.

(d) The overlap "gives" the reduced density matrix is now clarified to
the overlap "equals" the reduced density matrix. I also make more explicit
my hint. I've removed the confusing bits involving |Psi_{N-1}>; part (c)
is useful, but not directly applicable.
    I've also reorganized the hints, and separated the discussion of 
how the reduced density matrix relates to conductivity.
    I've mentioned explicitly that the four terms you get are after both
operators are shifted by one position.

F.3 Localization

A substantive error on my part: I used both N and L to represent the length
of the one-dimensional array. (Sorry for the confusion.) I now just use L.

I deleted the subscript N on Psi_N. It's really the same wavefunction as Psi.

I've added subscripts to the definition of K:
  "K(i,j;t) = exp(−iHt)_{ij}"

I've added a clarification above part (b) about K(i,j;t):
  "You can think of i and j as corresponding to positions x, x′ in the
  more traditional propagator (notationally we have changed
  K(x′, t′, x, t) → K(i, j; t′ − t))."

(c) The reference to 'equation 10' used to point to the wrong 
equation. It now points properly to the matrix Hamiltonian.

(g) I'm now more specific: calculate G_ij rather than 'calculate G', and
'maximum distance m for non-zero matrix element G_{n,n+m}' and such.
    Made it clear that I want a formula for the Green's function.

(h) The product should range from j=1 to M+1, not M-1.

(i) My reference to 'some constants' was for an earlier version of the
exercise.

F.4 Eight-fold way

The charge Q in figure 3(a) is a linear combination of I_3 and strangeness.

The proton and neutron have I_3 = +- 1/2 (not I).

(d) I've deleted the part about showing why the figure has 60 degree
angles, replacing it with a sentence above explaining the relation
to the symmetry group. 

The revised hint still reads
  "Note that the isospin operator in I3 V+|Σ−⟩ evaluates the isospin of a
  neutron, while in V+ I3|Σ−⟩ it evaluates the isospin of the Σ−."

(e) I've clarified the question by summarizing it at the end:
  "(That is, give the decomposition of the representation of SU(2) given 
  by the three quark directions of eqn 14 into irreducible 
  representations, and show that they are isospin 0 and isospin 1/2.)"
  I've also added that it should follow pretty much from the definitions.

(Old f): I've now eliminated this part, giving the longwinded argument for
the distributive property. (It didn't involve much quantum mechanics anyhow.)
Parts (g) and (h) are re-labeled (f) and (g).