Dara Stepanek
Thermodynamics, Quantum Mechanics, and General Relativity
HW #20
Due: Friday 5/13
1. What is absolute zero? Why was it a different flavor of physics from what Newton offered?
2. What is the zero-point energy? How can this force of nothing exist?
3. Heisenberg’s Uncertainty Principle (HUP) says ΔxΔp ≥ ђ/2. Given the General Uncertainty Relation
ΔAΔB ≥ |<[A, B]>|, prove HUP.
Things to recall and/or note:
- The right side of the inequality reads “the absolute value of the expectation value of the
commutator of the operators A and B”.
- The expectation value of a commutator implies that it is acting on a function.
- The commutator [A, B] = AB-BA.
- Bold-faced variables are operators.
- X=x and P=-iђ(d/dx).
- ђ is just a constant and i is imaginary.
4. Mathematically describe a black hole.
5. Give the mathematical analogy we used in class to explain why quantum mechanics and relativity
yield different or meaningless results for the exact same problem.