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Quantum physics

1 Amplitudes

Annotations:

- Follows from max possible knowledge of system

1.1 Complex #'s

1.2 Born Rule

Annotations:

- Born Rule: Probability of event = |psi|^2

1.3 IFM

Annotations:

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

2 Uncertainty

Annotations:

- Universe in very real sense, unknowable

2.1 Heisenberg

Annotations:

- 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.

2.1.1 Planck's
length
(h)

2.2 Feynman quote

Annotations:

- "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

3.1 Waves

3.1.1 Wave eqation

3.1.1.1 Schroedinger Equations

3.1.1.1.1 Operators

Annotations:

- A mapping between vectors; A vector function

3.1.1.1.1.1 hermitian

Annotations:

- A linear vector operator

3.1.1.1.1.2 Hilbert Space

Annotations:

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

3.2 Particles

Annotations:

- Individual particles unpredictable; lots of them follow statistical/ probabilistic laws

3.3 Feynman quote

Annotations:

- exhibits different behavior at different frequencies

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