Great student questions generated from Postulates of Quantum Mechanics readingPosted: September 10, 2011
In my 3rd year (intro to ) Quantum Mechanics course the first homework assignment I gave them was meant to serve as a mostly gentle review of probability and modern physics as is relevant to the first chapter of Griffiths.
But I also asked them to read an 8-page section of some supplemental notes prepared by Michael Dubson and Steve Pollock at CU-Boulder (they can be found in the “Lecture Notes” folder of the “all course materials EXCEPT assessments” link on this page). These notes talk explicitly about the postulates of quantum mechanics (which Griffiths does not), about postulates in general and they compare and contrast classical and quantum mechanics.
As part of that first homework assignment I asked my students to read these notes and gave them the instructions:
Please write one or two questions that were burning in your brain after you read these pages.
And they gave me some wonderful questions which should provide us with some rich discussion on Monday. Here they are:
- I’m very confused how a wavefunction can change instantly after a measurement has been made on it’s position. (note: several variations of this question showed up)
- What reasoning did Schrodinger have for writing down his equation? (note: several variations of this question showed up and one student noted that it looked a lot like an equation he had seen in our PDEs course)
- Why is gravity proving to be so difficult to incorporate into quantum theory?
- Do quantum and classical mechanics agree with each other in predicting the outcomes of physical phenomena at a particular intermediate scale between the quantum scale and the macroscopic scale?
- Why does Planck’s constant have that specific value?
- Does the wavefunction ever reconstruct itself after being collapsed due to an observation?
- How come taking measurements changes the look of the wavefunction? It almost looks like a dirac delta function in the after measurement graph shown.
- (edited for brevity) Since real-world sized objects are made up of large quantities of microscopic particles shouldn’t the (quantum) laws and properties that govern the small not also govern the behavior of the large, which are really just big groups of the small? Why would we get different physics looking at many than looking at one?
- If x and p are not well-defined for a point particle, how does putting a group of them together suddenly make them defined for the group? how many does it take? Two? Three? Four billion trillion? At what point does a system become macroscopic?
- Where did the notion of wave-particle duality originate?
- How valid is string theory and a fundamental level?
- How does a measurement give the particle a definite position?
- How does Psi-squared represent the probability that a particle is at a specific location when we are told that Psi only “carries information about the particle, it is not ‘the particle’ or ‘the position of the particle'”?
Fantastic! Now they’re curious. And I’m not great at establishing a framework that ties together the ideas in a course, but I think that these questions mostly provide that framework and it was them that generated it instead of me. It’s their framework! I am thrilled.