Consider a novel harmonic oscillator in which the hamiltonian operator takes the form where α and at satisfy the anti-commutation relations: use these anti-commutation relations to show the following: (a) show that h2 hh. what are the possible eigenvalues of h? hint: there are two eigenvalues. (5 points) (b) show that there must be a state annihilated by å. call this state po, such that αφο-0. (3 points) (c) show that φο cannot be annihilated by à, ie, that àtqbo 0. let φ1 ξ àton (3 points) (d) show that àol-фо, and àtdy-0. (3 points) (3 points) (f) suppose an electron is in the infinite potential well with length l. the electron is only allowed to be in the ground state, or the first excited state. if we want to use the ladder operators a and a to describe our system and write its hamiltonian as eq. (1), what should be the value of hw? (3 points) hint: the eigen-energy of electron in infinite potential wel for the n-th eigen- state: en-npr2h2/(2ml? )

Part a determine the magnitude of the x component of f using scalar notation. fx f x = nothing lb request answer part b determine the magnitude of the y component of f using scalar notation. fy f y = nothing lb request answer part c determine the magnitude of the z component of f using scalar notation. fz f z = nothing lb request answer provide feedback figure1 of 1a force vector acting on a ring attached to the ground is shown in the xyz space together with its x, y, and z components lying on the corresponding positive axes. the ring is located at the origin. force f is located in the first octant. f makes an angle of 60 degrees with its x component and an angle of 45 degrees with its y component. a force vector acting on a ring attached to the ground is shown in the xyz space together with its x, y, and z components lying on the corresponding positive axes. the ring is located at the origin. force f is located in the first octant. f makes an angle of 60 degrees with its x component and an angle of 45 degrees with its y component.

A17,250 kg rocket is pushed with a thrust of 6,450,284 n. what is the acceleration of the rocket?

Which are advantages of renewable resources? check all that apply. renewable energy supplies are completely reliable everywhere. some renewable resources will never be used up. little or no waste is produced by renewable resource plants. electricity can be generated in large quantities. many renewable energy facilities have lower operating costs.