Time-independent perturbation theory. (a) explain the need and the scope of application (b) if a perturbation is introduced a a,+with a«1 expand eigenvalue of energy and cigenfunction to produce three schrödinger equations (se) for the 0-th, 1-st, and 2-nd order in (c) expressing eigenfunction as a liner combination of the eigenfunctions of the unpertubed se derive the first order correction to the eigenenergy (d) using similar approach, derive the second order correction to the eigenenergy (e) derive the new perturbed eignefunction corrected to the first order

Rank the torques on the five doors shown in the figure above from least to greatest. note that the magnitude of all the forces is the same

The lights used by mark watley (played by matt damon) during the film the martian seem to be metal halide lamps. metal halide lamps are filled with vaporized mercury and metal-halogen compounds. when an electric current is passed through the lamp, the tube begins to glow a bright white/blue color. if you were to pass this light through a prism to separate the individual light frequencies, you would see a rainbow just as you would if using natural sunlight because of the complexity of the metal halide gas and the vast amount of possible electron transitions. (the study of light in this way is known as spectroscopy and allows astronomers to know exactly what atoms compose distant stars, simply by looking at the light they emit. the spectral lines an atom produces uniquely identifies that atom just like a fingerprint uniquely identifies a person. the momentum equation and energy equation that we have used above can be combined to give the following equation: c = e p where again p is the phonon momentum, e is the photon energy and c is the speed of light. when you divide the photon energy found in #6 by the photon momentum found in #4, do you get the speed of light? (if not, check your work for questions #4 through #6). yes no

Which articulations allow for greatest range of motion?