Recent content by fab333

I have a system described by the Langevin equation da/dt = - dF/da* + r where a are complex amplitudes of electromagnetic modes (and r is the white noise). How if F was real, it would be the Hamiltonian of the system, but in my case (and in general), F is complex (because the a are...

I'm trying to solve a system of five nonlinear equations (degree 7) in Mathematica: Solve[{q (a^2 + b^2 (3 q^2 + r^2 + 8 t^2)) ((e - q)^2 - R^2 - 4 T^2)^2 + q ((e - q)^2 + R^2 + 4 T^2) - 2 (e - q) (r R + 4 t T) == 0, R (a^2 + b^2 (3 R^2 + (e - q)^2 + 8 T^2)) ((e - q)^2 -...

I do not understand how to calculate the formula in first attachment. Can anyone help me? thanks

What are the conditions for which it can be concluded that a system has discrete energy levels? For example a system in one dimension with the potential V(x)=b|x| has only a discrete spectrum. How I can prove it? My book says moreover that the energy eigenvalues have to satisfy the...