Homework Statement
Hi, so I have been given the following operator in terms of 3 orthonormal states |Φi>
A = |Φ2><Φ2| + |Φ3><Φ3| - i|Φ1><Φ2| - |Φ1><Φ3| + i|Φ2><Φ1| - |Φ3><Φ1|
So I need to determine whether A is unitary and/or Hermitian and/or a projector and then calculate the eigenvalues and...
Homework Statement
Hi, I am really struggling with this Campbell-Hausdorff formula. The question requires me to use it to prove
ei/h omega.L (x , p) e-i/h omega.L = R(omega).(x, p) where L is the momentum operator, x and p are the position and momentum operator respectively and R(omega) is the...
Homework Statement
How do I use the commutation relations of su(2) and so(3) to construct a Lie-algebra isomorphism between these two algebras?
Homework Equations
The commutation relations are [ta, tb] = i epsilonabc tc, the ts being the basis elements of the algebras. They basically have the...
Thank you very much andrewkirk this helped, It would have been very straight forward indeed to just match up the coefficients because I then did the matching after the long inner product calculation and my answers matched.
I used each of the psis to take inner product with the function ##f##...
Homework Statement
Hi, am having difficulty with the Linear algebra in QM. We have been given a problem set and one of the questions am struggling with is as follows:
Consider the space of all linear functions ##f(x) = ax + b## (x real) defined over the range ## -1 < x < 1 ##, with the scalar...