Prove the following identities that we assumed to calculate [h, x] in [h, p] in class. (a) let a, b and c be arbitrary matrices (possibly infinite dimensional) then prove the following commutator identity: [ab, c] = a[b, c] + [a, c]b . (b) show that the position-momentum commutator [x, p] = i~ generalizes to [x n , p] = i~nxn−1 . (c) assume that f(x) has a convergent taylor expansion, then show that [f(x), p] = i~ df dx (x) .

Alarge truck is moving 22.0 m/s. if it’s momentum is 125,000 kg • m/s, what is the trucks mass

When temperature of a substance increases, of its particles increase resulting in more between particles. real world applications of thermal expansion absolute zero (-273 degrees c) is the lowest possible temperature on the kelvin scale. it is a measure of where a substance has no kinetic energy. heat is a process of the . energy flows spontaneously from a object to a until equilibrium is reached. heat is measured in heat is transferred throughis a method of heat transfer that occurs between particles of matter that are in direct contact with each other. are poor conductors that impede / reduce the rate of heat transfer. is a method of heat transfer that occurs in fluids (non-solids) by means of currents. real world application of convectiona method of heat transfer through electromagnetic waves. when energy moves from one object to another inside a closed system, no energy is or in the system in the transaction. systems will spontaneously move to a state of organized energy or high disorder over time called

For this car, predict the shape of a graph that shows distance (x) versus time (t). note that time is the independent variable and will be on the bottom axis. need asap