M1L3e.txt

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Now we want to go deeper into the quantum domain
by talking about the spin 1/2 Hamiltonian.

So in other words, we want to go beyond expectation values.
We want to talk about the wave function itself.
So the Hamiltonian, which we will
use for major parts in this course,
it's one of the fundamental Hamiltonians in physics.
Of course, there is the harmonic oscillator,
there is the hydrogen atom, but then there
is this Hamiltonian, which is a two level system with splitting
omega 0, and then we make a simplification where
we use pure exponentials-- so a single frequency in complex
notation, with a complex exponential,
e to the i omega t as the derived term.
So this is one of the simplest Hamiltonians
for this kind of system.
It's a two level system with a splitting,
and now it is driven, and the simple strive term is not
cosine omega t or sine omega t, as we will see,
the simple strive term is e to the i omega t.