There are several aspects of QM we will need to understand
as general concepts.
Quantum states form a vector space (Hilbert space).
- A QS can be written as a linear combination of other
forks can be represented as a string of local pressures (snaps)
can be decomposed using the Fourier transform (tuning forks)
sets of states can form a basis
vectors one can compute an inner product.
- Orthogonality: No overlap between QS. This implies
that the states are chosen to be completely distinct in some way. There
is a label that can be used to completely distinguish state 1 and state
State can share some characteristic. Two states may both have some
likelihood of being at some location.
Operators may represent observables so their behavior and
interpretation tells us how to think about particle properties.