Heisenberg Uncertainty Principle and Debroglie Wavelength and Operators
In-Class Worksheet
Problem 1- The average speed of a helium atom at 25 C is 1.23x103m/s. What is the average wavelength of a helium
atom at this temperature. How does this compare to the size of a helium atom (140pm)?
Problem 2- Heisenberg Activity
A) How do the tennis balls effect the heavy object?
B) How do the tennis balls effect the light object?
C) All analogies relating to quantum mechanics are imperfect. The only real way to discuss it is to understand the
complex mathematics. However this is a great way to get an understanding for how it works. We should still recognize
where the analogy does not follow reality. Where does this analogy “fall apart”?
Question 3- Which statement(s) are correct according to the Heisenberg Uncertainty Principle. (Note: Light does have
momentum, although its not calculated by its mass (it has no mass) but rather by its wavevector, something we won’t go
into in this class, you just need to know that it does have momentum to answer this question)
A) You cannot simultaneously know the velocity and position of matter
B) You cannot simultaneously know the momentum and position of matter
C) You cannot simultaneously know the momentum and position of light
D) It exists because our measurements are not accurate enough
E) It exists due to the duel nature in all things
Heisenberg Uncertainty Principle and Debroglie Wavelength and Operators
Question 4- Use the Heisenberg uncertainty principle to calculate the uncertainty in meters in the position of a
honeybee weighing 0.68g and traveling at a velocity of 0.85 m/s. Assume that the uncertainty in the velocity is 0.10m/s.
How does this compare to the size of the bee?
Heisenberg Uncertainty Principle and Debroglie Wavelength and Operators
Question 5- Some math help. Operators are often not something that is familiar to students. Before watching the next
video it is useful for you to have an understanding of this mathematical concept, even if we won’t be actually doing the
math.
Note: Normally I highly suggest googling things for extra help. This is an exception, if you google this, you are likely to only find
extremely high level math. If such things interest you, then google away. But note, nothing more complicated than what I show in
the videos, worksheets and sapling will be tested on. Also note: this is an over simplification designed to help you understand what
is happening. If you go on to physical chemistry you will see the more accurate version of this.
Definition of “operator”: a function acting on the space of physical states
over-simplify that to: a function that acts on a particular type of function instead of a number
Definition of eigenvalue:non-zero vector that when a matrix is multiplied by it yields a constant multiple
over-simplify that to: the number that is returned when a particular operator (Hamiltonian) acts on a particular function
(eigenfunction), such that the same function, times a number, is given back.
A) Lets do an example, that while too simple to mean much physically, will hopefully get the point across:
If an operator is “multiply by 3” and the equation is 4x. Operate on the equation and state what we would call the eigen
value if we were using the appropriate functions.
B) Now let’s do one that is a bit more physically relevant, even if not for our particular case. If we have a vector
v=1x+2y+3z we can act on it with a parity transformation. The parity operatorvis commonly used to describe when you
flip the signs of 3 dimensions in a vector. I.e. change the sign of each x, y, z coordinate. Write down the new function.
What would be one possible eigenvalue for this?
Challenge Question:
C) Calculus isn’t required in this course, however if you know how to do it, this is a better and more relevant example.
Try it, see how it works. If you don’t know what a derivative is, then don’t worry about it.
The kinetic energy portion of the Schrodinger equation involves the following operation for one dimension
Act on the following function with the operator. Assume L and n are constants.