Hour Exam #2 Review Sheet and Sample Exam

Hour Exam #2 Review Sheet and Sample Exam - REVIEW GUIDE...

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REVIEW GUIDE FOR HOUR EXAM #2—ECE 352—B. SKROMME Problems will be similar to the HW; you will definitely have a problem involving the derivation of density of states functions in one, two, or three dimensions, using either periodic or standing wave boundary conditions. You will also have at least one problem involving wells and/or barriers. 1. Having found ( x ) in a well or barrier problem, how do you find ( x , t )? 2. When is ( x ) continuous? When is ′( x ) continuous? 3. When is it possible to separate the time-dependent Schrödinger equation into equations for ( x ) and ( t )? 4. Suppose ( x ) = A exp –( x / ) 2 , where is a constant. How would you find A ? 5. What is the definition of transmission and reflection coefficients in quantum mechanics? How are they related? 6. What happens to the wavelength of an electron when it enters a region of higher potential energy (where it still propagates)? 7. What is the probability density current of an evanescent wave? 8. When is the allowed energy spectrum of an electron continuous? When is it discrete? 9. Is the wave function ( x ) = A exp –( x / ) 2 localized? Why or why not? 10. What is the group velocity of a standing wave? 11. What is tunneling? 12. How many spatial quantum numbers are there in most three-dimensional problems? 13. What is the physical significance of l ? of m l ? 14. If 1 l l , how does f ( ) behave? 15. Which quantum number(s) determine the energy of an electron in a H atom? In a more complicated atom? 16. Find the ground state electronic configuration of Se (atomic number 34). 17. Do particles with spin 2 obey the Pauli exclusion principle? Do spin 5/2 particles? Which kind of statistics applies to each? 18. Describe the assumed form of the potential energy inside a crystal in the quantized free electron model. 19. Compare and contrast standing wave boundary conditions with periodic boundary conditions. Which is best for studying conductivity? 20. Define the term Fermi level . What fixes it in a metal? 21. Should electrons scatter from ion cores in a crystal in the free electron gas model? Do they experimentally? 22. How does the shape of f FD ( E ) change with temperature? 23. Is E F strongly dependent on temperature in a metal?
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