The problem given is a perturbation on the two dimensional harmonic oscillator where the perturbation is simply: H'=-qfy.
It seems that all of the elements of the matrix H' are zero and so constructing a diagonal matrix in the subspace is eluding me. Any ideas?
Consider this senario. The pion is initially at rest in its frame. The pion has a certain amount of rest energy mc^2 and when it decays into photons all of this energy is converted into the momentum of the photon E=pc. In order to uphold conservation of momentum, if the pion with initial...
In part (b) I get as far as solving for v(t), but to solve for x(t) I'm left with the integral of (1/(x^3 + x0^3)). Is very messy and ends up being tan-1(some function of x) + ln(another function of x). Because of that I can't solve for just x in terms of only t.
Homework Statement
A particle of mass m is acted on by the forces as given below. Solve these equations
to find the motion of the particle in each case.
(a) F(x, t) = k(x + t2), with x = x0 and v = v0 = 0 when t = 0;
(b) F(x', t) = kx^2 x', with x = x0 and v = v0 = 0 when t = 0;
(c)...