May12Lecture

May12Lecture - Pauli exclusion principle The overall...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Pauli exclusion principle The overall wavefunction Ψ (space AND spin) must change sign when swap the quantum numbers of any 2 electrons Consequence: no two electrons can have the same set of quantum numbers . Ψ ab = - Ψ ba 1st slot: electron 1 quantum numbers (space and spin) 2nd slot: electron 2 quantum numbers For two electrons, the possible wavefunctions are: Ψ = ψ sym χ anti Ψ = ψ sym χ anti OR ψ sym = [ ψ n ( x 1 ) ψ m ( x 2 ) + ψ m ( x 1 ) ψ n ( x 2 )]/2 1/2 ψ anti = [ ψ n ( x 1 ) ψ m ( x 2 ) - ψ m ( x 1 ) ψ n ( x 2 )]/2 1/2 " anti = [ # 1 $ 2 %$ 1 # 2 ]/2 1/ 2 sym = [ # 1 $ 2 + $ 1 # 2 ]/2 1/ 2 " 1 " 2 " 1 " 2 “singlet”: total S= 0 ( both spins; each has individual spin quantum number S=1/2) 3 “triplet” states, each with total S=1 Quantum numbers of electrons 1 and 2 are swapped
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

May12Lecture - Pauli exclusion principle The overall...

This preview shows document pages 1 - 2. Sign up to view the full document.

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