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? )