## Quiz #1.

Completion of this quiz before September 6 can give you up to 2 credit points.

1) In soving a particular problem you decide whether to use quantum or classical mechanics by:

a) using DeBroglie's relation to find the wavelength of the object and if it is greater than a normal linear dimension of the problem you should use quantum mechanics
b) using the uncertainty principle to find the imprecision in position, and if it is large then you must use quantum mechanics
c) using the uncertainty principle to find the imprecision in momentum, and if is is small then you must use quantum mechanics
d) using DeBroglie's relation to find the wavelength and if it is smaller than 1 nm you must use quantum mechanics.

2) Which of the following statements is wrong about Hermitian operators:

a) the eigenvalue of a Hermitian operator is a real number
b) if two linear Hermitian operators have the same set of eigenfunctions then they commute
c) eigenfunctions of a linear Hermitian operator either are orthogonal or can be made orthogonal to each other
d) a Hermitian operator can be a complex operator
e) two different Hermitian operators cannot have the same set of eigenfunctions

3) For the photoelectric effect (emission of electrons upon irradiation of a metal sample with light in a vacuum), which of the following statements is correct?

a) The number of photoelectrons emitted depends on the frequency of the light (assuming that the light has enough energy to overcome the work function).
b) The kinetic energy of the photoelectrons emitted depends linearly on the frequency of the light.
c) The intensity of the light has no effect on the number of photoelectrons observed.
d) The kinetic energy of the photoelectrons increases as the frequency of the light squared.
e) The work function of the metal will depend on the frequency of the light.

4) Which pair of operators does not commute, i.e. [A,B] = AB-BA is not 0::

a) x and d/dx
b) x2 and eax
c) x and y
d) x and x
e) x and d/dy
f) more than one from above

Please make comments about the lectures this week or anything else concerning the class. It is optional, you can submit your answers first and then your comments separately.

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