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Problem 6.25Classical Electrodynamics (3rd)John David Jackson
In James walker 3rd edition physics, in the figure 22-36 c shows a rectangular loop, carrying a current I, that is in a magnetic field pointing out of the page. Could the magnetic field shown be created by the current in the loop? Why or why not?
A Particle in a boxIn order to answer the following questions you will need toconsideran infinite potentialwell of length L, in which a particle has been confined.1. For principal quantum number n=7, write code to calculatethenormalization constant.Then, plot the probability density function for this state (usingL= 10).2. Using the properly normalized wave equation from Question1,write code to determinethe expectation values <x> and <x2> . Is <x>oneof the most probable positions? Explainwhy.3. Using the properly normalized wave equation from Question1,write code to determinethe expectation values <p> and <p2> . Show the valueyouobtain for <p2> is equal to2mE7 (where E7 is the energy of the n = 7 level). Remember that pisa differentialoperator so you will have to use the diff command.4. The uncertainty of a quantum measurement is defined on page222,Equation 6.41 (3rdedition SMM). Using this equation calculate the uncertainties oftheposition andmomentum of a particle in the n = 5 state. Compute the productofthese uncertainties andcompare this with the prediction of the Heisenberguncertaintyprinciple.Quantum oscillator5. Repeat calculations in the previous question for the groundstatewave function of thequantum oscillator. Comment on the obtained result.
and . Show the valueyou obtain for is equal to 2mE7 (where E7 is the energy of the n = 7 level). Remember that pis a differential operator so you will have to use the diff command. 4. The uncertainty of a quantum measurement is defined on page 222,Equation 6.41 (3rd edition SMM). Using this equation calculate the uncertainties ofthe position and momentum of a particle in the n = 5 state. Compute the product ofthese uncertainties and compare this with the prediction of the Heisenberg uncertaintyprinciple. Quantum oscillator 5. Repeat calculations in the previous question for the groundstate wave function of the quantum oscillator. Comment on the obtained result.
