Consider a quantum system wtih three states, and a hamiltonian given by 0 3 4 with ε a small parameter and vo and η are constants. we assume η 0. (a) write the eigenvalues e and eigevectors in0)) of the unperturbed hamiltonian (c = 0) for n = 1,2,3. (b) find the three first-order energies, e for n 1,2,3, due to the perturbation e. (c) find the first-order correction to the three eigenstates, in(1), with n = 1,2,3 ( d set vo = 1 (in units of energy) and η = 0.5. plot the three energies ) and the three energies en) for small e, with n = 1,2,3. (e) set vo-1 and η = 0.5. plot the three components of ln(iy for small ε for n = 1. in the plots, you need to decide how far to plot in ε, since ε must be a small parameter.

For problems 1-3, consider a simple dc brush motor with a permanent magnet stator. with an an consider a simple dc brush motor with a permanent magnet ae supply voltage of 100 v, the no-load speed of the motor is 1000 rpm. this motor can provide a torque of 1.9 n-m at 800 rpm drawing a current of 2 a current are both zero at no load.) 1. with an armature supply voltage of 100 v, the motor is operated at 900 rpm. what is the motor torque? what is the mechanical power delivered by the motor? what is the current draw? what is the electrical power input? what is the energy efficiency of the motor? with an armature supply voltage of 100 v, the motor is operated at 1100 rpm (where it acts as a generator). what torque input is required? what mechanical power is required what current is generated? what is the electrical power generated? what is the energy efficiency of the motor acting as a generator? 2. with an armature supply voltage raised to 120 v, the motor is operated at 1000 rpm. what is the no-load speed? what is the motor torque? what is the mechanical power delivered by the motor? what is the current draw? what is the electrical power input what is the energy efficiency of the motor? 3.

Frank just graduated from eighth grade. assuming exactly four years from now he will graduate from high school how many seconds does he have until his high school graduation

Global warming will produce rising sea levels partly due to melting ice caps but also due to the expansion of water as average ocean temperatures rise. to get some idea of the size of this effect, calculate the change in length (in m) of a column of water 1.45 km high for a temperature increase of 1.12°c. assume the column is not free to expand sideways. as a model of the ocean, that is a reasonable approximation, as only parts of the ocean very close to