Nuclear Fusion Physics and Technology/Atomic Physics summary

Definition: Linear Harmonic Oscillator Hamiltonian Linear Harmonic Oscillator Hamiltonian of a particle is defined as where operators Definition: Anihilation Operator Anihilation Operator is defined as Definition: Creation Operator Creation Operator is defined as Theorem: a, a+ compound expressions Lets assume Linear Harmonic Oscillator Hamiltonian. Then Proof: Directly form a, a+ definitions with respect to LHO Hamiltonian definition and [x,p] commutator Theorem: H,a,a+ commutators Lets assume Linear Harmonic Oscillator Hamiltonian. Then Proof: The first expression may be evaluated from commutator definition directly from a, a+ compound expression theorem The second and the third expressions needs first, which can be obtained from a,a+ compound expression theorem again: