Woops i made a mistake! d=4^n not d=4n. So that the direct sum method of fundamental reps will not work. Instead i was thinking of this: Is, for example
\mathbb{R}^4\otimes\mathbb{R}^4\cong\mathbb{R^{16}} ?
Then the tensor product of the fund (or trivial) rep with itself is also a rep of R^16...
It cannot be this long, because this question is part of question from a past exam paper. Either there is a mistake in the question and the R^d should actually mean
\mathbb{R}\otimes\mathbb{R}\otimes\cdots\otimes\mathbb{R}
d times(in which case the question is ok) or there are reps of the...
I assume that the electron is orbiting the nucleus, you can use a certain equation to find the force on the electron, and you know how many protons copper nucleus has. use this to find the velocites.
One way of solving a pde like that is to always try separation of variables , so that you assumeu(x,t)=X(x)T(t)where X is just a function of x and T just a function of t, plug this into your pde and see what u get!
Sometimes the 2pi is written on the outside like you did or sometimes it is incorporated into the exponential as e^{-2i\pi sx} (substitution in the integrand then gets you from the 2pi in the expo to the outside). Make sure that it is of the same form in your book.
Homework Statement
i) Show that the Lorentz group has representations on any space \mathbb{R}^d
for
any d = 4n with n = 0, 1, 2, . . .. Show that those with n > 1 are not
irreducible. (Hint: here it might be useful to work with tensors in index
notation and to think of symmetry...
Homework Statement
The Lagrangian of a non-relativistic particle propagating on a unit circle is
L=\frac{1}{2}\dot{\phi}^{2}
where ϕ is an angle 0 ≤ ϕ < 2π.
(i) Give the Hamiltonian of the theory, and the Poisson brackets of the ca-
nonical variables. Quantize the theory by promoting...
Yes i have decided to take your advice on board and instead focus more heavily on the mathematical framework needed to develope a quantum theory for matter. Perhaps I can then do a short chapter on quantum liquids, that way i can still learn and apply some condensed matter physics.
But i still...
Thank you very much for the advice. Indeed it could be a very big problem if i start then halfway something goes wrong. That is why i want to start early, within a month i want to finish the introduction.
March is the deadline for choosing the project for us, even if something goes wrong i...