[SOLVED] QM: system with two lin. independent states 1. The problem statement, all variables and given/known data Imagine a system with just two linear independent states: [tex]|1>=(1,0)[/tex] and [tex]|2>=(0,1)[/tex] (these are actually column matrices, but I don't know how to type those in tex) [tex]|\Psi>=a|1>+b|2>=(a,b)[/tex], also [tex]|a|^2+|b|^2=1[/tex] suppose the hamiltonian is a 2x2 matrix with entries j,g above and g,j below, [tex](g,j \in R>0)[/tex]. The time-independent schroding equation reads [tex]H |\Psi>=i h/(2 pi) d/dt(|\Psi>)[/tex] a) find the eigenvalues and eigenvectors of this hamiltonian b) suppose the system starts out at t=0 in |1>, what is the state at time t? 3. The attempt at a solution I thought of solving the time-independent SE; [tex]ja+gb= i h/(2 pi) d/dt(a)[/tex] [tex]ga+jb= i h/(2 pi) d/dt(b)[/tex] but does this mean g=0? And if so, how do I get any further. I'm stuck.