PHYS212 : Homework |
Quantum Review and the Infinite Square Well
(b) How does your result from part (a) compare with the corresponding probability for a classical particle bouncing back and forth in a region of width ? Specifically, does the quantum mechanical result reduce to the classical result in the classical limit ( )?
(a) Find the probability density and the overall normalization constant of the superposition. (Use the normalized forms of and .)
(b) The probability density is time dependent. Use Maple to animate it. You will need the plots package
[> with(plots):Then, if you define the function and limits
[> rho := (Your density function of x and t) ; [> L := (well width) ; [> tmax := (duration of the animation in fs) ;the animation syntax is
[> animate(rho, x=0..L, t=0..tmax);
(c) Calculate the expectation value of . (Feel free to have Maple do the integrals.) It is also time dependent. Use Maple to graph it over an appropriate time interval.
(d) Describe in words what your animation of part (b) and your graph of part (c) tell you, and how they relate to each other.
Copyright © 2003-2009, Lewis A. Riley | Updated Tue Apr 14 02:04:45 2009 |