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 QS.
• Tuning forks can be represented as a string of local pressures (snaps)
• Snaps can be decomposed using the Fourier transform (tuning forks)
• Certain sets of states can form a basis
• As 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 2.
• Overlap: 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.