phy-4600/concepts

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2016-03-26 00:08:04 +00:00
the meaning of an operator - how it relates to an action that is a measurement and also an action on the state
the meaning of an eigenstate and an eigenvalue for an operator
the concept of a complete set of orthogonal operators that commute
- this says something about having common states
superposition states
unitary operators:
❙Ψ❭ = ∑ ❙n❭❬n❙Ψ❭ = ∑Cₙ❙n❭
❬n❙Ψ❭ = ∫ dx ❬n❙x❭❬x❙Ψ❭
= ∫ dx n†(x) Ψ(x)
time evolution
schrodinger equation - specific cases: infinite or finite well, harmonic oscillator, hydrogen atom
angular momentum operators