PHYS 301           Study Guide for Part III                Ch. 6, 7, and 8

This is meant to help you review for test #3. You will be tested mostly on what was covered and worked out in class. Use you lectire notes as a guide when you study. The go to you book and the links listed below for details.

Ch. 6: In Chapter 6, the emphasis is the inroduction  and solution of the Schrödinger's equation for simple cases.

bulletYou should be able to write the general solution for  Schrödinger's equation for the particle in an infinite well.
bulletYou should then be able to  apply boundary conditions and eliminate one of the terms in the general solution.
bulletYou should also be able to apply the normalization condition and deternine the constant for you solution.
bulletYou should then be able to calcualte energy eigenvalues (energy levles En , n=1,2,3 ...)
bulletYou should also be avle to calculate  prbability for finding the particle at any given n.
bulletYou should be  able to calcualte expextatiob values for position <x> and momentum <p>

Ch. 7 Barriers and Walls: Tunnelling and Barrieer Penetration (slides 1-17)

    In ch. 8, Particles incident on a finite potential barrier (section 8-1) and particles bound in a finite potential well (8-5)  are   dealt with.

  1.     Study examples 8-1 (page 209) and make sure you understand what T and R represent.   
  2.     Study example 8-2 (page 212) is this a realistic example, Can a truck tunnel through a bump?
  3.     Be able to explain why alpha deacy (section 8-4) is a good example of tunneling.
  4.     Read about the ammonia molecule (page 214) expalin how its behavior is realted to tunneling.
  5.     Read about the scanning tunneling microscope. Be able to explain how it works (page 218-219)   

Terms you should know and be able to state what they are in words as well as mathematically.

Normalization of a wave function,     Boundary condition,     continuity condition,    tunnelling,      barrier penetration

expectation value,    eigenfunction,    eigenvalue,   the many expressions of Heisenbergs Uncertainity principle, application for tunnelling,

Ch. 8 Quantum Mechanics in 2 & 3D

bulletYou should be able to write the general solution for  Schrödinger's equation for the particle in an infinite well in 2 and3d
bulletYou should then be able to  apply boundary, conditions and eliminate one of the terms in the general solution.
bulletYou should also be able to apply the normalization condition and determine the constant for you solution.
bulletYou should then be able to calculate energy eigenvalues (energy levles En , n=1,2,3 ... i x , y and z dimensions)
bulletYou should also be able to calculate  probability for finding the particle at any given n
bulletYou have to know the difference between the approaches Bohr and Scrodinger used to deal with the hydrogen atom.
bulletHow do the results obtained by solving  the Scrodinger equation for the hydrogen atom compare eight that of the Bohr model?
bulletWhat are the four quantum numbers associated with the electron in the hydrogen atom?
bulletBe able to understand and reproduce example 9-3 on page 243.
bulletGiven a radial wave function of the from given in equation 9-39 (page 243) be able to determine at which r the probability for finding the electron peaks (i.e. becomes a maximum).