Basical questions of quantum, neglect 2 due to extra frame please.

1 The formalism of quantum mechanics (8 points) a) Write the definition of a Hermitian operator. [1 point] b) Prove that the momentum operator is Hermitian. [2 points] c) Do the position operator i and the momentum operator p have a set of common eigenstates? Motivate your answer. [1 point] d) Write the commutation relation between the position operator + and the momentum operator p. [1 point] e) Express mathematically Heisenberg's uncertainty principle and verify it based on your answer from point d). [2 points] f) Comment on the implications Heisenberg's uncertainty principle on measurements. [1 point] 2 Time-independent perturbation theory (4 points)