573lec29 - 5.73 Lecture #29 29 - 1 Begin Many-e Atoms:...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
29 - 1 5.73 Lecture #29 updated September 19, Begin Many-e Atoms: Quantum Defect Theory See MQDT Primer by Stephen Ross, pages 73-110 in Half Collision Resonance Phenomena in Molecules (AIP Conf. Proc. #225, M. Garciá-Sucre, G. Raseev, and S.C. Ross) 1991. turning points of for Vr e rr rn an n n n l hll l ll l () , / =− + + + ≈± + << ± 22 2 0 2 2 12 0 2 2 1 11 1 1 2 m * * * * Last Time: * μ n l (r) rR n l (r) dominated by small lobe (n-independent nodal position) at inner turning point, amplitude scales as n–3/2, and large lobe at outer turnin point (essentially all of the probability. envelope ur pr nn / EI P n n n n l l l −− 2 1 1 2 nodes: radial nodes angular nodes total nodes gives spacing between radial nodes λ expectation value scaling (see below) (H - atom energy levels) n n σ σ σ σ σ <− ≥+ 1 1 1 3 2 2 geometric mean of expectation values of r for off - diagonal matrix elements when is n n nn n n n n l ( ) [] =′ ++ ′′ 2 2 2 2 // (? ) σ σ σ σ
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
29 - 2 5.73 Lecture #29 updated September 19, TODAY 1. Many-e atom treated as core plus outer e that sees shielded core as Z(r). 2. l -dependent energy shifts n-independent quantum defects 3. energy shifts are actually phase shifts in u n l (r) relative to u n l (r) for H-atom 4. Rigorous QDT EI P n n n l l =− −µ () 2 A. regular and irregular Coulomb functions f,g satisfy Hydrogen-like Schr. Eq. OUTSIDE core B. Boundary conditions at r C .πµ l is a phase shift repeated patterns in each integer region of ν D. Multi-channel QDT µ matrices e colliding with core can also transfer energy and angular momentum to core-e noninteger values of require mixture of and find satisfies boundary condition number of members in series of © s with integer spacings, constant quantum defect ν ν ν µ ∞∴ E nr n l l 12 / fg * channels rather than eigenstates * focus on dynamics, but in a “black box” way. Dynamics happens within a restricted region of space. This region of space is always sampled, regardless of E, in the same way. Everything is determined by the boundary conditions for the outgoing wave.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.

Page1 / 10

573lec29 - 5.73 Lecture #29 29 - 1 Begin Many-e Atoms:...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online