Chem 539 Weekly Quiz 1

Quiz #1

deadline is August 28 (midnight)

Completion of this quiz gives you 2 credit points depending on the correctness of your answers. Instructions: You may take as long as you want to complete this quiz but you must work alone. It might be a good idea to have both your lecture notes and your text handy. Please note that if Student ID is wrong, or you submit your answers after the deadline then no credit will be given.

1) If a wavefunction y is a linear combination of the eigenfunctions of the operator A : y = Sc_if_i ( where A|f_i> = a_i|f_i> ) , the expectation value of A equals <A> = <y|A|y>. Assuming that f_i are orthonormal, i.e. <f_i |f_j> = d_ij (i.e., 0 unless i = j), the calculated value of <A> should means:

a) the result of repetitive measurements that will always be the same and equal <A>
b) the results of measurements will vary randomly but the average value will be equal <A>
c) the results of measurements will be one of the a_i with the probability given by |c_i|²

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

a) x and d/dx
b) x² and e^a^x
c) x and y
d) x and x
e) x and d/dy

4) The wavefunctions of an electron in a quantum mechanical system (in Schrodinger position representation) are related to :

a) The charge density in a particular region of space.
b) The probability density of measuring an electron in a particular region of space.
c) The amplitude of the electric field in a particular region of space.
d) The intensity of the electric field in a particular region of space.
e) The probability of measuring an electric field in a particular region of space.

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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Please note that if Student ID is wrong, or you submit your answers after the deadline then no credit will be given.

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