Consider a quantum system with just three linearly independent states. suppose the hamiltonian, in matrix form, is (1-) 0 0 where vo is a constant and e is some small number, e 1 write down the eigenvectors and eigenvalues of the unperturbed hamiltonian, (e a) b) solve for the exact eigenvalues of h. expand each of them as a power series in e up to second order. c) use first and second order non-degenerate perturbation theory to find the approximate eigenvalue for the state that grows out of the non-degenerate eigenvector of h. compare the exact result from part b). d) use degenerate perturbation theory to find the first-order correction to the wo initially degenerate eigenvalues. compare the exact results.

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.

co2reflects heat radiation back to earth buning coal and oil emits co2 globe warms

their crystal patterns have been disrupted by stress