Question

Consider a particle of mass m moving in a one-dimensional potential of the form V. for 0<x<b, V(a) = 0 for Islal<e, for 1212, with V., b and c positive constants and c>b. a Explain why the wave function of the particle can be assumed to be cither an even function or an odd function of a. b For the case that the energy E of the particle is in the range 0<ESV., find the (unnormalized) even cigenfunctions and give an equation that allows to determine the corresponding energy cigenvalues. (You do not need to solve the equation for the energy cigenvalues. Also note that some part of the cases 0<E<V, and E=V, must be solved separately.) C Assume that the energy cigenvalue of the lowest even cigenfunction is exactly V. Show that this determines V. uniquely as a function of b and e. a For the lowest even cigenfunction considered in part )compute the proba- bility of finding the particle in the interval 05:30 HINT: The calculation of the normalization of the eigenfunction involves an integral of the form ſ sinº(+)d:. This is most easily computed after rewriting cos? ( 3 ) = (1 + cos(2:))

Answer 1

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