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simple quantum mechanics exam questionHi, I just want to ask a simple question about quantum mechanics... This question appears in it's original form here: [Only registered and activated users can see links. Click Here To Register...] (question 2)I have had a go and put some notes into the text below... I am stuck on parts c) (ii) and (iii). Any help much appreciated! Thanks. _______________________________________________ A quantum mechanical system is described by a two-dimensional state space spanned by the orthonormal vectors |1> and |2>. The Hamiltonian of the system can be defined by: H|1> = a|1> + 2a|2> H|2> = 2a|1> + a|2> with "a" a positive constant. (a) Write down the matrix representation of H in the basis {|1> |2>}. Easy: (a 2a) (2a a ) (b) Find the energy eigenvalues of the systems and associated orthonormal eigenvectors. I get {3, 1/root2*(1,-1)} and {-1,1/root2*(1,1)}, where this has been expressed in the form {eigenvalue,eigenvector}. (c) If at time t = 0 the system is described by the state vector |2>: (i) Find the mean value of the energy <H> at time t = 0. I get <H> = a. (ii) What is the probability that the system will be found having its highest possible energy at time t = 0? (iii) If the highest energy is measured at time t = 0, calculate the state vector of the system at time t. _________________________________ Any ideas? Thanks! Chris. |

simple quantum mechanics exam questionHi, Chris, Haven't you forgotten something here? Do you know what the equation is for the variation of psi with time? Write it down, solve it, and then find the values of the unknown coefficients by equating the general solution at t=0 to the known initial condition. The correct answer to this question is clearly: Wonderful, wonderful Copenhagen Friendly old girl of a town 'Neath her tavern light On this merry night Let us clink and drink one down To wonderful, wonderful Copenhagen Salty old queen of the sea Once I sailed away But I'm home today Singing Copenhagen, wonderful, wonderful Copenhagen for me I sailed up the Skagerrak And sailed down the Kattegat Through the harbor and up to the quay And there she stands waiting for me With a welcome so warm and so gay Wonderful, wonderful Copenhagen Wonderful, wonderful Copenhagen Friendly old girl of a town 'Neath her tavern light On this merry night Let us clink and drink one down To wonderful, wonderful Copenhagen Salty old queen of the sea Once I sailed away But I'm home today Singing Copenhagen, wonderful, wonderful Copenhagen for me Cite it in full and you will get full marks, but do not so much as breathe the words "Hund's paradox" or the name "Shahriar S. Afshar". Cheers, Zigoteau. |

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