Quantum physics

Nota:

• Follows from max possible knowledge of system

1. Complex #'s
2. Born Rule

   Nota:

   • Born Rule: Probability of event = |psi|^2
3. IFM

   Nota:

   • IFM: Interaction Free Measurement Answer to HW1 problemhttp://logicaltightrope.com/2013/08/13/seeing-without-looking-the-quantum-bomb/

Nota:

• Universe in very real sense, unknowable

1. Heisenberg

   Nota:

   • 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.
   1. Planck's length (h)
2. Feynman quote

   Nota:

   • "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.

1. Waves
   1. Wave eqation
      1. Schroedinger Equations
         1. Operators

            Nota:

            • A mapping between vectors; A vector function
            1. hermitian

               Nota:

               • A linear vector operator
            2. Hilbert Space

               Nota:

               • Complex-valued linear vector space; Complete space w/ an inner product
               • Inner Product: generalized dot product (?)
2. Particles

   Nota:

   • Individual particles unpredictable; lots of them follow statistical/ probabilistic laws
3. Feynman quote

   Nota:

   • exhibits different behavior at different frequencies