The Hamiltonian of a three-level system in a chosen basis
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Linear algebra and vector spaces · Linear algebra and vector spaces
Error, Chance and the Machine, Ch Iteration: nonlinear systems and eigenvalues
Problem
The Hamiltonian of a three-level system in a chosen basis, in eV, is H=50.500.530.200.2−1.
((a)) Write down the three Gershgorin discs for H, giving each as a lower and upper bound in eV.
((b)) State what the discs allow you to conclude about the sign of each energy eigenvalue, before doing any further computation.