A small .40 kg cart is moving back and forth along an air track between two bumpers that are 2 m apart on the air track with a constant speed of .50m/s by treating the cart as a quantum particle, estimate the value of the principle quantum number that corresponds to its classical energy

Asquare 1m x 1m plate is shown below. all four of its edges are kept at 0 co. at t=0the temperature distribution is given by: y xtsins n75)=.a) using separation of variables determine the temperature distribution t(x,y,t)along the plate at any time t.b) discretize the heat conduction equation +=22222 txtusing a second-order centered difference scheme for the two second derivatives and a first-order forward euler scheme for the first derivative. using von neumann stability analysis, determine the stability criterion for the proposed discretization scheme in terms of , hand t. solve for the maximum allowable time step tmax