# The Mr Tompkins Quantum Mechanics Assignment

15 Mar 1996 // science

Mr Tompkins will help you understand quantum mechanics. He is just like an ordinary man, only quantum.

Question 1. If Mr Tompkins replaced the suspension of his car with quantum harmonic oscillators, what is the probability of him scraping the diff on a speed hump?

Question 2. If Mr Tompkins is facing a firing squad and army marksmen were using electrons as bullets, then, (a) what will be the spread of the bullet's gaussian wavefunction if the range is 10m? (b) what will be the probability that Mr Tompkins is in an alive eigenstate at a time t after firing? (c) if the ten bullets are fired simultaneously use perturbation theory to find the effect they have on one another as they travel.

Question 3. Mr Tompkins throws himself off the leaning tower of Pisa. What is the uncertainty in the distance between his head and his neck if we take s(t=0) as the length of his neck at time t=0, and, what is the probability of him tunneling to the other side of the earth?

Question 4. Mr Tompkins is put into a mental institution with 6 feet concrete walls. On average, how many times will he have to head butt the wall to tunnel through and escape?

Question 5. Mr Tompkins travels at the speed of light for 40 years and comes back home. If he has sex with his graddaughter, is it strictly paedophilia? (Hint: take into account time dilation).

Question 6. Mr Tompkins wants to use the twin paradox to live forever. How fast does he have to go, and, how much does he have to soup up his Honda Civic if c = 100 km/hour?

Question 7. Mr Tompkins is having marital problems with his wife. What is the distance R for the Van der Waals attraction to give him a decided advantage the next time he ventures to his bedroom?

Question 8. Mr Tompkins has been drinking a few too many (n>1) beers. The alchohol is giving him a head spin. What is the spin-orbit coupling between his head and any convenient brick walls?

Question 9. Assuming Bose-Einstein statistics, if Mr Tompkins farts into a bottle, to what temperature must he cool the liquid for it to form a Bose condensate superfluid? Bonus marks: for what practical applications can this superfluid be used for?

Question 10. Mr Tompkins tries to perform a parity operation on himself. Does this constitute a gender transformation? If so, is the operation invertible, and, find a dimensionless ladder operator to convert Mr Tompkins from male to female. (Hint: the operator does not include the use of a scalpel). If not, what is wrong with Mr Tompkins?

Question 11. Mr Tompkins uses the orthogonality principle on matrices to produce degenerate eigenstates of himself. Show that the linear combination of his eignenstates cannot possibly constitute a complete state and that due to interference, something is missing (Hint: Mr Tompkins and intelligence are operators that don't commute).