1Fri. Mar. 30, 2007 Phy107 Lect 281From Last Time…Atoms:quantized orbitsquantized energiesquantum states labeled by integers n=1,2,3…Atomic spectra: photon emission and absorptionFri. Mar. 30, 2007 Phy107 Lect 282Classical vs quantumLow classical amplitude, lowenergyHigher classical amplitude,higher energyFri. Mar. 30, 2007 Phy107 Lect 283Probability density of oscillatorMoves fast here,low prob of finding in a‘blind’ measurementMoves slow here,high prob offindingClassical probFri. Mar. 30, 2007 Phy107 Lect 284Zero-point energy• In all cases, wave represents the quantum-mechanical nature of the particle.• In all cases, the lowest energy state representeda particle with some motion.• The particle can NEVER sit still.• This also comes from the uncertainty principle– If the particle were sitting still, it’s momentum wouldbe accurately zero.– Means that position is completely uncertain.Fri. Mar. 30, 2007 Phy107 Lect 285Unusual wave effects• Classically, pendulum withparticular energy neverswings beyond maximumpoint.• This region is ‘classicallyforbidden’• Quantum wave functionextends into classicallyforbidden region.Classicallyforbidden regionEnd ofswingFri. Mar. 30, 2007 Phy107 Lect 286• Quantum mechanics predicts someprobability of the pendulum being foundbeyond the limits of it’s swing!• This is a common effect in quantummechanics, arising from wave nature ofparticle.2Fri. Mar. 30, 2007 Phy107 Lect 287Particle in a box, againLWavefunctionProbability =(Wavefunction)2Particle contained entirelywithin closed tube.Open top: particle can escape ifwe shake hard enough.But at low energies, particlestays entirely within box.Like an electron in metal(remember photoelectric effect)Fri. Mar. 30, 2007 Phy107 Lect 288Quantum mechanics sayssomething different!In quantummechanics, there issome probability ofthe particlepenetrating throughthe walls of the box.Low energyClassical stateLow energyQuantum stateNonzero probability of being outside the box!Fri. Mar. 30, 2007 Phy107 Lect 289Two neighboring boxes• When another box is brought nearby, theelectron may disappear from one well, andappear in the other!• The reverse then happens, and the electronoscillates back an forth, without ‘traversing’the intervening distance.Fri. Mar. 30, 2007 Phy107 Lect 2810The tunneling distanceLow probability‘high’ probabilityFri. Mar. 30, 2007 Phy107 Lect 2811Example:Ammonia molecule• NH3• Nitrogen (N) has two equivalent‘stable’ positions.• It quantum-mechanically tunnelsbetween 2.4x1011 times per second(24 GHz)• Was basis of first ‘atomic’ clock(1949)NHHHFri. Mar. 30, 2007 Phy107 Lect 2812Atomic clock questionSuppose we changed the ammonia molecule sothat the distance between the two stablepositions of the nitrogen atom INCREASED.The clock wouldA. slow down.B. speed up.C. stay the same.NHHH3Fri. Mar. 30, 2007 Phy107 Lect 2813Tunneling between conductors• If one well is a little deeper than the other, the particletunnels and then stays in the other well.• The well can be made lower by applying an electric field.• This is the principle used in a scanning tunnelingmicroscope.Fri. Mar. 30, 2007 Phy107 Lect 2814Scanning Tunneling Microscopy• Over the last 20 yrs, technology developed to controllably positiontip and sample 1-2 nm apart.• Is a very useful microscope!Fri. Mar. 30, 2007 Phy107 Lect 2815Can we see atoms?Fri. Mar. 30, 2007 Phy107 Lect 2816L.J. Whitman, Naval Research LaboratoryFri. Mar. 30, 2007 Phy107 Lect 2817STM image analysis• The tip is scanned acrossthe sample, recording the z-position at each point.Fri. Mar. 30, 2007 Phy107 Lect 2818Silicon• 7x7 surfacereconstruction• These 10!nm scansshow the individualatomic positions4Fri. Mar. 30, 2007 Phy107 Lect 2819Surface steps on SiImages courtesyM. Lagally,Univ. WisconsinFri. Mar. 30, 2007 Phy107 Lect 28207x7 + steps• 7x7 unit cell structure on theterracesFri. Mar. 30, 2007 Phy107 Lect 2821Atomic wires from Si stepsCaF grown uniquely atstep edgesMolecular wires, 3 nm diameterfrom ferrocene precuresorImages courtesy F. Himpsel, Univ. WisconsinFri. Mar. 30, 2007 Phy107 Lect 2822Will atomic wires/particles be thenext generature storage media?Image courtesy F. Himpsel, UWFri. Mar. 30, 2007 Phy107 Lect 2823Scanning Tunneling Microscopy• Over the last 20 yrs, technology developed to controllably position tip andsample 1-2 nm apart.• Is a very useful microscope!Fri. Mar. 30, 2007 Phy107 Lect 2824Manipulation of atoms• Take advantage of tip-atom interactions tophysically move atoms around on the surfaceD. Eigler (IBM)• This shows the assemblyof a circular ‘corral’ bymoving individual Ironatoms on the surface ofCopper (111).• The (111) orientationsupports an electronsurface state which canbe ‘trapped’ in the corral5Fri. Mar. 30, 2007 Phy107 Lect 2825Quantum Corral• 48 Iron atoms assembled into a circular ring.• The ripples inside the ring reflect the electron quantum states ofa circular ring (interference effects).D. Eigler (IBM)Fri. Mar. 30, 2007 Phy107 Lect 2826The Stadium CorralAgain Iron on copper. This was assembled to investigate quantum chaos.– The electron wavefunction leaked out beyond the stadium too much to to observeexpected effects.D. Eigler (IBM)Fri. Mar. 30, 2007 Phy107 Lect 2827Some fun!Kanji for atom (lit. original child)Iron on copper (111)D. Eigler (IBM)Carbon Monoxide manCarbon Monoxide on Pt (111)Fri. Mar. 30, 2007 Phy107 Lect 2828More unusual aspects ofquantum mechanics• Quantum jumps: wavefunction of particle changesthroughout all space when it changes quantumstate.• Superposition: quantum mechanics sayswavefunction can be in two very differentconfigurations, both at the same time.• Entanglement: two quantum-mechanical objectscan be intertwined so that their behaviors areinstantly correlated over enormous distances.Fri. Mar. 30, 2007 Phy107 Lect 2829The wavefunctionand quantum ‘jumps’• A quantum system has only certain discretequantum states in which it can exist.• Each quantum state has distinct wavefunction,which extends throughout all space• It’s square gives probability of finding electron ata particular spatial location.• When particle changes it’s quantum state,wavefunction throughout all space changes.Fri. Mar. 30, 2007 Phy107 Lect 2830Hydrogen atom• Hydrogen a little different, in that it hasspherical symmetry• Not square like particle in a box.• Still need three quantum numbers, but theyrepresent
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