A) Calculate the mean values <x^2> and <p^2x> for stationery state n. B) Calculate the rms...
1. Consider a particle of mass m in an infinite square well with potential energy 0 for 0 Sz S a oo otherwise V (x) For simplicity, we may take the 'universe' here to be the region of 0 S z S a, which is where the wave function is nontrivial. Consequently, we may express stationary state n as where En is the associated mechanical energy. It can be shown that () a/2 and (p:)0 for stationary state n. (a)...
1. Consider a time-homogeneous Markov chain X)n, such that P= 2 a) Calculate p12(2) b) Assuming Xo 1 (with probability 1), find the probability that Xn will reach state 2 before it reaches state 4 c) Find msz. d) Is the chain periodic? Irreducible? e) Find the stationary distribution f Approximate the probability that X0 1 g) Find the mean recurrence time for state 1