A) consider two observables represented by operators a and b. show that it is possible b if and only if a commutes with b to choose a complete set of eigenfunctions which are sharp in both a and for simplicity, you may assume that the eigenvalues of a are non-degenerate. [4] (b) how operators compatible with the hamiltonian can be used to resolve the degeneracy consider an example of a highly degenerate set of energy eigenfunctions. explain

Explain the difference between each pair of concepts. a. frequency and relative frequency b. percentage and relative frequency a. select the correct choice below. a. frequency is the total number of observations in a data set. relative frequency is the number of times a particular distinct value occurs. b. frequency is the number of times a particular distinct value occurs. relative frequency is the ratio of the frequency of a value to the total number of observations. c. frequency is the total number of observations in a data set. relative frequency is the ratio of the number of times a particular distinct value occurs to the frequency. d. frequency is the number of times a particular distinct value occurs. relative frequency is the ratio of the frequency of two different values.

15. one purpose of the tread pattern on a tire is to a reduce tire wear. b. reduce traction c. allow water to flow away from the tire. d. look impressive.

As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. when you push the platform, you compress the springs. you do an amount of work of 79.0 j when you compress the springs a distance of 0.230 m from their uncompressed length. (a) what magnitude of force must you apply to hold the platform in this position? (b)how much additional work must you do to move the platform a distance 0.230 m farther? (c) what maximum force must you apply to move the platform a distance 0.230 m farther?