What about the third case? my first though would be that since U(r(vector))=U(r^2(scalar)) then it is independent of any rotational angle (theta, phi) then angular momentum is conserved for all space. Is this true?
If I rotate around the x axis, the x coordinate should remain unchanged then should it not, therefore the angular momentum in the x direction is conserved?
For the second case, would this mean that we are solely dealing with the xy plane, thus a rotation around the z axis leaves the system...
I've been asked to find the conserved quantities of the following potentials: i) U(r) = U(x^2), ii) U(r) = U(x^2 + y^2) and iii) U(r) = U(x^2 + y^2 + z^2). For the first one, there is no time dependence or dependence on the y or z coordinate therefore energy is conserved and linear momentum in...
Homework Statement
Light of intensity I0 passes through two sets of apparatus.
One contains one slit and the other two slits. The
slits have the same width. What is the ratio of the out
going intensity amplitude for the central peak for the
two-slit case compared to the single slit?Homework...