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Example
Essay Questions
Below are examples of essay questions
that have been asked as part of the New Model Course in Applied
Quantum Physics.
Explaining
devices and experiments
- The photoelectric tube we studied in
class last week has some unusual properties as a circuit element,
including behaving for some voltages as if it had a negative
resistance". (Note: By "negative resistance" I
mean that for some values of V, "R" = V/I is negative.
On our IV curve for the phototube we actually had positive current
at a slightly negative voltage.) What is the difference between
what is happening to the conduction electrons in the photoelectric
tube as compared to what happens to them in a resistor?
- Describe briefly Rutherford's experiment
probing the structure of the atom and explain why the result
was a surprise.
- A researcher tells you that within a
10 second window, a single electron will hit the television screen
you are viewing. Sure enough, there is a flash within that time
window. The researcher told you nothing else, though, and so
you don't know the experimental setup being used. You only know
that she has a gizmo that allows the release electrons at long
time intervals. Do you know if that electron went through a two-slit
interference apparatus or if it was simply shot at the screen?
Explain how you arrive at your answer.
- An electron and a proton of identical
energy are incident on the same potential barrier. If the probability
of transmission for the electron greater than, less than, or
equal to the transmission probability of the proton? Explain
how you arrived at your answer.
- What is the difference between a conductor
and an insulator? Give experimental evidence for the descriptions
that you give, and try to account for these descriptions using
a microscopic model of the material.
- Based on the model we have been describing
in class, how could you account for the difference between a
conductor and a resistor... Explain.
- How, if at all, can you account for
the different conductivity values of different types of metals?
Does copper conduct better, or does iron? How do you know? Explain
how you think about the situation.
- An LED (light emitting diode) is a device
like the one in your VCR remote control and many other appliances.
When observed, it seems to shine in only one color. Is there
a filter in the glass or is it a property of the device? Explain
how you could account for the observation, based on what you
know about the device. If you don't know anything about LEDs
(I'm guessing that's the case for many of you), tell me, and
then STILL try to figure out what might be going on. Use your
everyday physics thinking on this one, if you don't know the
formal response...
- We have talked about the LED and we
have talked about polarization of metals. Compare and contrast
the two. Compare the "current" electrons in the case
of the LED and the polarized metal. What are the similarities
and what are the differences? How do you know? Explain in as
much detail as possible.
Interpreting
representations
- Consider the n=1 and n=2 states of an
electron located in an infinite square well potential. You know
that the electron is in one of those two energy levels, but you
don't know which. In making a measurement of the particle's location
one afternoon in the lab, you find the following: it's located
exactly in the middle
of the well.
a) how can you account for this? what do your
measurements tell you about the energy of the electron?
b) you repeat the experiment. What do you expect
to find this time?
Explain.
- Often, wave functions and potential
barriers are shown on the same graph (the text does this a lot).
Is it possible for a particle described by a wave function whose
crest is LESS than the height of a square potential barrier to
be transmitted through a barrier? Explain.
- In class we discussed the probability
of finding a particle in one or the other well, when two wells
are placed close to each other. If we placed TWO particles in
the two wells at the lowest possible energy and assumed that
they don't interact with each other, what then? Describe the
probabilities of finding the particles in well L (left well),
well R (right well), or both wells. How did you arrive at your
answer? (note: This calls on you to interpret the wave function
pictures drawn in class, and what the various plots mean... do
the best you can to describe things verbally, if at all possible.)
Discussing
open-ended issues - fishing expedition questions
- Do you think a photon is more like a
wave or more like a particle? Explain why you think so.
- In the infinite square well potential,
there are often places (in excited states) where the probability
of finding a particle is zero. Does that mean that a particle
can't move through that location? Explain (i.e. explain how we
can measure the location in one probable area, then later measure
it in another probable area separated by a place where the probability
was zero).
- You have a friend taking this class
at another university, and her class is slightly ahead of this
one. She calls you up one day and says, "You won't believe
my crazy prof, he's so funny and always has us laughing. It's
the greatest. But you know what he told me? He said that there's
nothing we can do about it, quantum mechanics is the real way
of thinking about the world, and all that stuff we learned in
our intro classes was all wrong." What do you tell her,
should she agree with the prof or not? Do you? Back up your answer
with examples from your previous studies of physics.
- When did you first learn about electrons
and that electrons were particles which were parts of atoms?
Elementary school, high school, college? From teachers, from
magazines, from TV? Do you even remember when you learned it?
How do you know that it's true? This is one of those questions
to help me see where you stand, so you don't have to say too
much. I'm just curious when and how you learned some of the things
you're bringing to class.
- A friend of yours is taking a class
like this one at another school. She calls you up one day and
you get to talking about your classes. She says, "we just
talked about the probability of finding particles in a potential
well, and I think I figured it out. Whaddya think, the particle
is always located somewhere, but we sometimes simply can't measure
it. Even if we're not always paying attention to it, it's still
located somewhere, right? That makes sense to me..." What
do you tell her? Do you agree? disagree? Be as thorough and explicit
as possible.
- A friend (not the same one who has stopped
calling you, a different one...) talks to you in the hallway
of the student union. You're being nerdy and talking about conduction
in wires. He says the following, "When I have a wire, and
it's not in an electric field or anything, it doesn't have any
current, so there are no free electrons. There aren't any in
the wire until an electric field, you know, a voltage or something,
is on the thing. Then you get free electrons." Does his
thinking agree with yours? How is it similar, how is it different?
If it is similar, explain in more detail what your friend might
be saying. If it is different, explain how you think about the
existence of free electrons in a metal.
- A friend in your math class tells you
that when doing quantum mechanics you don't have to think about
classical things at all. It's either quantum or it isn't. When
you do quantum, you just have to toss your intuition out the
window and let the math and the weird stuff take over. Rather
than simply reacting to this statement, I want you to give me
TWO examples. As part (a), give me an example where your friend
is CORRECT, and you had to suspend all understanding of classical
mechanics in order to think about the quantum physics. In part
(b), give an example where your friend is INCORRECT, and you
had to use your classical reasoning to help you with the quantum
mechanics.
Relating
quantum physics to classical physics
- We often talk about the "probability"
that something might happen. a) Give some examples from real
life, and some examples from physics. For example, we could talk
about the probability of events in classical physics (what's
the probability that something is within 5% of its peak height?),
but we often don't. Why is that? b) Why should we think about
probability in the case of quantum mechanics and the physics
of the very small?
- The Heisenberg uncertainty principle
is a fundamental quantum principle. Would you expect there to
be something similar for sound waves? analog electrical signals
sent over a wire (standard telephone)? Explain why or why not.
- Suppose that the electron in the hydrogen
atom obeyed classical mechanics rather than quantum mechanics.
Why should this hypothetical atom emit a continuous spectrum
rather than the observed line spectrum? Explain.
- The Bohr model is based on several assumptions.
Discuss them and discuss their significance. Specifically, point
out those that contradict classical physics, and how they do
so.
- A large particle (i.e. use classical
physics) is located in an infinite potential well made up of
two very hard walls. In other words, the particle is bound and
will be located between the two walls. The question is, what
are the forces acting on the particle at any given time? Where
is there an acceleration and what direction are the forces on
the particle? Explain.
- When we think about a particle in a
box (i.e. an infinite square well), we find that the squared-momentum
(i.e. p^2) has distinct and constant values, while the momentum
itself (i.e. p) does not. Explain how this can be, and draw parallels
to the classical motion of a particle.
Extending
and interpreting lessons from the classroom
- In the tutorial on Friday, we discussed
how to localize an electron in space (somewhat) at a fixed instant
of time. If we want the electron to move in the +x direction,
how would we modify what we have done? What determines the speed
of each of the component waves and what determines the speed
of the electron?
- To describe a localized electron traveling
through space, we have to think of many different values of k
(meaning many different values of p). In the tutorial, we described
an electron and its location at a fixed moment in time (i.e.
t=0 in an equation of both x and t). How would we have to change
the equations we wrote in the spreadsheet to take time into account?
Would the velocity of each term of our wave be the same? Explain.
- If you made observations on a series
of electrons each of which was in a state with wavefunction psi,
how would you calculate the average momentum that you would measure?
- Richard Feynman, a famous physicist,
once said that "electrons arrive in lumps, like particles,
but the probability of arrival of these lumps is determined as
the intensity of the waves would be. It is in this sense that
the electron behaves sometimes like a particle and sometimes
like a wave." Elaborate on this in your own words, including
examples from how light behaves. I expect that you'll return
to the tutorial for your response.
- An electron bound in an atom has both
a kinetic energy and experiences a force so it has a potential
energy. Consider the electron's kinetic, potential, and total
energies. Are they positive, negative, or zero? Explain how you
arrived at your answers.
- In an infinite well, a particle is bound
to a fixed region in space. Imagine that it is moving back and
forth with a kinetic energy, KE. Consider this particle's total
energy. Is the total energy positive or negative? (hint: Does
your answer depend on the value of the potential energy? how
do we determine that? where is the PE zero?)
- For a quantum mechanical particle moving
under the influence of a finite, localized potential, we refer
to negative energy states as "bound". Why? Give as
much detail as possible about such a state (i.e. about things
that are always true for such a state, no matter the shape of
the well). Also, describe the sign of other states of the system...
- In discussing the three dimensional
box, we end up with an equation for psi with three directions
and time, also. Consider that the wave function starts in the
ground state. A change is made to the system (energy is added),
and the wave function in the x direction changes. What effect,
if any, does this have on the wave function in the y direction?
Explain how you think about the situation.
- In this week's homework, we are using
the energies of photons emitted by a system to tell us something
about the character of the system. When we observe photon energies
emitted by a system, what kind of energy of the system is relevant?
Listening
to general commentary
- As you have studied for the exam, you
have most likely encountered ideas that caused you great difficulty.
Please tell me which idea or concept has been most difficult
to understand and why it has caused you problems. Be as verbose
as you'd like, but don't be too brief...
- In the previous question, I asked you
to talk about an individual topic from the class, but in this
question, I'm asking you to evaluate your overall knowledge of
the material. You probably expect (or hope) to get a certain
grade on this exam, and I've found that people are usually good
(well, excellent) at knowing how to evaluate themselves. How
do you think you will do on this exam? Explain why you think
so.
- You have been doing a lot of reading
on your own, doing homework on questions that I haven't even
talked about in class, and so on. Could you comment on this style
of learning the material? The question gets to the issue of "do
you mind having this be like a literature class, where I assume
you are doing the reading?"
- Many of you have covered topics like
semiconductor physics and so on in other classes. Could you please
tell me (using names, not numbers, since I don't know those for
EE and ChemE and all) in which classes you have discussed band
diagrams, charge flow, current, transistors, and so on.
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