Orbital Angular Momentum
Hamiltonian Defined by
Where is the Hydrogen-like atom Hamiltonian:
Total angular momentum is defined by:
where
for electron For hydrogen atom Hamiltonian with energy level
NB: $m$ in above equation is **not mass**, $m_{0}$ is mass.
Intrinsic Spin
Spin in QM has no analogy in classical dynamics
Consider case where there is no angular momentum,
Contribution to Hamiltonian from spin:
Where is the spin quantum number. For an electron, the spin values can be
“g value” for intrinsic spin for electrons is 2. For protons is 5.6
What is g value?
Hydrogen Hamiltonian is comprised of the potential term, kinetic term, spin term and angular momentum term.
Silver screen experiment
MRI
Hamiltonian for Spin
for protons
Gives use to 2 level system in both
In class 26.1
Conventional Computing has binary digits (0,1)
Transistor: insert photo of transistor here
Either something goes through or not.
Quantum Computing:
You use the fact that quantum mechanical systems are a linear combination of many states. Instead of just 2 bits, you can have a large number of “qubits” that arise from the linear superposition of the two level states.
- 2 level systems denoted by and
Recall:
Block Sphere describes a superposition of states.
in matrix notation:
In class 2 & 3