Quantum Quantum Phenomena Phenomena

II:II:RevisionRevision

Chris Parkes April/May 2003

Hydrogen atomHydrogen atom Quantum numbers Electron intrinsic spin

Other atomsOther atoms More electrons! Pauli Exclusion Principle Periodic Table

Particle PhysicsParticle Physics The fundamental particles The fundamental forces

CosmologyCosmology The big bang The evolution of the

universe

Fundamental PhysicsAtomic Structure

http://ppewww.ph.gla.ac.uk/~parkes/teaching/QP/QP.html

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Quantum NumbersQuantum Numbers

Atom can only be in a discrete set of states n,l,mAtom can only be in a discrete set of states n,l,m Diff. From classical picture with any orbit

Principle n fixes energy - quantizedPrinciple n fixes energy - quantized Integer >=1

l fixes angular momentum Ll fixes angular momentum L Integer in range 0 to n-1

m (or mm (or ml l ) fixes z component of angular ) fixes z component of angular momentummomentum

Integer in range –l to +l

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Total Angular momentumTotal Angular momentum

1.1. Orbital angular momentum L, Orbital angular momentum L, e orbiting nucleuse orbiting nucleus L2=l(l+1)h

2.2. Quantum number lQuantum number l notation l=spdfg…., l=0,1,2,3,4…

3.3. ll has z-component mhas z-component mll,, (-l….+l) (-l….+l) Interacts with magnetic field, U=mlBB Zeeman effect gives splitting of states

4.4. Spin s=1/2Spin s=1/2, intrinsic property of electron, intrinsic property of electron Has ms =-1/2, +1/2 So splits an l state into two

5.5. Total Angular Momentum JTotal Angular Momentum J Sum of orbital and spin Anomalous Zeeman effect / Stern-Gerlach Expt

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Energy levelsEnergy levels

Hydrogen Energy levels Hydrogen Energy levels 1/n 1/n2 2 , scale is eV, scale is eV

In a magnetic field E will depend upon other In a magnetic field E will depend upon other quantum numbers (mquantum numbers (mll,m,mss), for Zeeman effect this ), for Zeeman effect this is:is:

[For anomalous zeeman effect from electron spin it is[For anomalous zeeman effect from electron spin it is

Where g is gyromagnetic ratio ~ 2]Where g is gyromagnetic ratio ~ 2]

eVn

E2

6.13

BmU Bl

BgmU Bs

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Energy Levels cont..Energy Levels cont..

For multi-electron atomsFor multi-electron atoms Energy splitting depends on l even in absence of Energy splitting depends on l even in absence of

magnetic field.magnetic field. occurs due to screening effect Central field approximation

Pauli Exclusion principlePauli Exclusion principle No two fermions in same state

……Structure of Periodic tableStructure of Periodic table

electrons

nucleus

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Particle PhysicsParticle Physics

Forces are due to exchange of the fundamental Forces are due to exchange of the fundamental force carrying bosonsforce carrying bosons

Photon,gluon,W+,W-,Zo (and presumably graviton)

Know the fundamental particlesKnow the fundamental particles Three generations of quarks and leptons

Don’t observe free quarksDon’t observe free quarks Confined in colourless hadrons

Added some more conservation lawsAdded some more conservation laws Energy, momentum, electric charge Baryon number, lepton number

Particle interactions can be written as Feynman Particle interactions can be written as Feynman diagramsdiagrams

Know the basic vertices, and conservation laws to see whether or not a reaction will occur.

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Particle interactionsParticle interactions

Some basic standard model vertices:Some basic standard model vertices:

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The Big BangThe Big Bang

Evidence for the Big BangEvidence for the Big Bang It is dark at night! See Olbers Paradox Universe expanding Cosmic microwave background Relative abundance of elements in universe

Universe Expanding – Hubble’s lawUniverse Expanding – Hubble’s law

Hence universe ~ 15 billion years oldHence universe ~ 15 billion years old

v = H x d,

Velocity Hubble const. distance

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Evolution of the universeEvolution of the universe

Controlled by Quantum PhenomenaControlled by Quantum Phenomena Early stages dominated by basic particle physics Later stages by gravitational effects

Starts at high temp., high densityStarts at high temp., high density Cools down and expands….Cools down and expands…. Key stagesKey stages

Separation of forces into the four basic forces Formation of nuclei Formation of atoms

Microwave background radiation, remnant photons from when atoms formed

Then gravitation dominates and stars and galaxies form