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
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