# What Does A Wavefunction Tell Us?

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Chemistry 21a
Midterm Examination
CLOSED BOOK SECTION
ONE HOUR
Allowed Materials:
• Your brain, paper, and a pencil or pen.
• You may not use notes, textbooks, electronic devices

DATE:
START TIME:
END TIME:

CLOSED BOOK
1. From the Postulates of Quantum Mechanics:
a) What does a wavefunction tell us? (In your answer, list three important attributes). b) What kind of operators represent physical observables? (In your answer, list three important attributes).
c) Write down the equation that gives the time evolution of a wavefunction.
2. Failure of Classical Physics
a) Two key relations that arose during the development of quantum physics were the DeBroglie equation and the Planck/Einstein relation. What were these? b) Give an example of an experiment that illustrates each relation and shows the failure of classical physics. Briefly explain the quantum mechanical behavior and why classical physics would have given an incorrect answer.

3. Operators
Show whether the following operators are Hermitian:
a. i
b. x
c.

!
!x

d. i x

!
(for a 2D Cartesian system of independent coordinates (x, y); you
!y

can use the previous results of this question if needed)
4. Orthogonality of Eigenstates
Using Dirac Notation, prove that if two eigenstates of a Hermitian operator are nondegenerate, then they are orthogonal.

Chemistry 21a
Midterm Examination
OPEN BOOK SECTION
TWO HOURS
Allowed Materials:
• Your class notes from this class.
• Your completed problem sets from this class, and the official solution keys. • The required text, McQuarrie (inside cover has useful constants and integrals) • All hand outs from class
• A table of integrals and constants. You may use the inside covers of a nonrequired textbook (for example, if you have a Math Methods book with a useful table of integrals, you may use it). Do not use any other textbooks.
• A calculator (four function or scientific). If you choose to use a more advanced calculator (graphing, computer algebra system), you may only use functions found on a typical scientific calculator (logs, trig, etc.). Do
NOT perform symbolic manipulation. Do not store text or programs on your calculator.

DATE:
START TIME:
END TIME:

OPEN BOOK
NOTE: TABLE OF CONSTANTS AND A FEW USEFUL
INTEGRALS CAN BE FOUND ON THE INSIDE COVERS OF TEXT
1. Diffraction by Matter
A student wants to see a diffraction pattern from a crystal of sodium, which has a lattice spacing of approximately 3 Angstroms. He has an electron gun which generates electrons of 3 ×107 m/s and an ion source which generates protons of 1×102 m/s.
a) What are the momenta of the particles?
b) Which source will better be suited for seeing a diffraction pattern?
2. Spectrum of Benzene