Quantum physics

Quantum physics

1. Amplitudes

   • Follows from max possible knowledge of system
   • Complex #'s
   • Born Rule
     • Born Rule: Probability of event = |psi|^2
   • IFM
     • IFM: Interaction Free Measurement Answer to HW1 problemhttp://logicaltightrope.com/2013/08/13/seeing-without-looking-the-quantum-bomb/

2. Uncertainty

   • Universe in very real sense, unknowable
   • Heisenberg
     • E= ~hw, p=~hk; ~h = h/2pi dx*dp \> h 
     • Trans: If you pinpoint the position of a specific particle, then you won't be able to precisely measure its momentum.
     • And if you precisely measure a particles momentum, then you cannot know its exact position
     • Also, if we try to measure the momentum of the wave, this uncertainty shows up with how accurately we can measure it - classical mechanics fails at this point.
     • Planck's length (h)
   • Feynman quote
     • "Yes! physics has given up. We do not know how to predict what would happen in a given circumstance, and we believe now that it is impossible - that the only thing that can be predicted is  the probability of different events.

3. Wave Particle duality

   • Waves
     • Wave eqation
       • Schroedinger Equations
         • Operators
           • A mapping between vectors; A vector function
           • hermitian
             • A linear vector operator
           • Hilbert Space
             • Complex-valued linear vector space; Complete space w/ an inner product
             • Inner Product: generalized dot product (?)
   • Particles
     • Individual particles unpredictable; lots of them follow statistical/ probabilistic laws
   • Feynman quote
     • exhibits different behavior at different frequencies