Answer Happy

Question 01: Consider a 1-dimensional quantum system of one particle in which the particle is under a potential V(x) = {mw?z?, with m being the mass of the particle and w being a parameter (you may take it as angular fre- quency) with inverse dimension of time. The particle may be found in the region -00<<0. • What is the averaged position at which the particle may be found while it is in the ground state? • What is the uncertainty in the position in the ground state? • What is the uncertainty in the momentum in the ground state? • See if Heisenberg uncertainty principle is varified at the ground state? • Calculate the probability that the particle make a transition to the first excited state under the operator 0 =qi. Varify that the lowest two states of the system are mutually orthonormal.