Quantum physics

Quantum physics

1. Amplitudes

   • Complex #'s
   • Born Rule
     • Born Rule: Probability of event = |psi|^2
   • IFM
     • FMI: interaction free measurement
   • Follows from max possible knowledge of system

2. Uncertainty

   • Heisenberg
     • Planck's length (h)
     • 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.
   • 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.
   • Universe in very real sense, unknowable

3. Wave Particle duality

   • Waves
     • Wave eqation
       • Schroedinger Equations
         • Operators
           • hermitian
             • A linear vector operator
           • Hilbert Space
             • Complex-valued linear vector space; complete space w/ an inner product
               • inner product: generalised dot product
           • a mapping between vectors; a vector function
   • Particles
     • individual particles unpredictable; lots of them follow statistical/probabilistic laws
   • Feynman quote
     • exhibits different behaviour at different frequencies