This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: HOMEWORK ASSIGNMENT 4 PHYS852 Quantum Mechanics I, Spring 2008 Topics covered: Atomic Physics applications: STARK EFFECT, Zeeman effect, spin-orbit coupling 1. [15 pts] Compute the Stark effect to lowest non-vanishing order for the n = 3 level of the hydrogen atoms. Fully evaluate whatever matrix elements, ( nm | Z | n m ) , appear. Also remember to identify the good states before applying perturbation theory. Include a sketch of the energy levels versus E , with each level labeled by its state(s). 2. [10 pts] Do the same as the previous problem, but for the Zeeman effect. 3. [5 pts] Prove that [ J z , vector L vector S ] = 0. Is m j is conserved in the spin-orbit interaction? 4. [10 pts] Let the hamiltonian H for some system depend on the parameter , so that H = H ( ). The eigenstates and eigenvalues are then also functions of , i.e. E n = E n ( ) and | n ) = | n ( ) ) . Expand H , the eigenvalues, and the eigenvectors around and use first-order perturbation theory (with...
View Full Document