PHYSICS 137A Midterm: physics137A-sp2014-mt1-Markov-soln
Document Summary
A particle"s coordinate space wavefunction (x) is real and square integrable. Prove that the particle"s average momentum is zero. A particle of mass m moving under the in uence of a one-dimensional potential v (x) has the wavefunction: That is, nd the value of n . E suppose that you nd out that v (x) = 0. F suppose instead that you only know that v (0) = 0 and you also do know that (x) is an energy. G explain why (x) is or is not the ground state wavefunction. That is, why e is or is not the lowest eigenstate. Find the potential v (x) and the energy eigenvalue e? possible energy eigenvalue. Suppose (x, t) obeys the one-dimensional schr odinger equation: A derive the conservation law for probability: = 0 where (x, t) = is the probability density and the probability current is given by: B explain why this equation is the conservation law for probability.
