2. GAIA: TEORIA KUANTIKOAREN

SARRERA

“Helburua ez da ikustea beste inork ikusi ez duena, baizik eta pentsatzea beste inork pentsatu ez duena guztiek ikusten ari garen gauza bati buruz.”

E. Schrodinger (1887-1961)

UHINEN EZAUGARRI BATZUK

(Newton-en 2.legea garatuz)

A2=A12+A2

2+2A1A2cos(1-2)

I=I1+I2+2(I1I2)1/2cos(1-2)

y=A sin(kx1-t)+A sin(kx2-t)

(Uhinen ekuazioa lineala delako)

(Argia uhin bat dela frogatzeko)

(Ezaugarri batzuk)

(2. ordenekoa eta lineala)

+

x2-x1=n

x2-x1=(n+1/2)

[ sin(a+b) = sina cosb + cosa sinb ]

sin(A+B) = 2 cos[(A-B)/2] sin[(A+B)/2]

UHINEN INTERFERENTZIAK

2 zirrikituen saiakuntza

Gainezarmena (ekuazioaren linealtasunarengatik)

T. Young

http://www.walter-fendt.de/ph14e/doubleslit.htm

(edo vG)

http://www.colorado.edu/physics/2000/applets/fourier.html

Euler: ei=cos+isin

UHIN GELDIKORRAK

1 dimentsiotan

2 dimentsiotan

PULTSOAK edo BATIDOAK

Dispertsioa (edo sakabanaketa)

v=v(x) (edo v())

v=ktea

Talde eta Fase abiadurak

http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/sines/GroupVelocity.html

UHINEN BESTE EZAUGARRIAK

Isladapena

Errefrakzioa

Difrakzioa

a

(Einstein-en erlazioa)

(de Broglie-ren erlazioa)

/k (uhinaren fase-abiadura) partikularen abiadura al da?

DAVISSON ETA GERMER-EN ESPERIMENTUA (1927)

Physical Review 30, 705 (1927)

W.L. Bragg

Zorizko aurkikuntza bat zen!

d=0.91 A

2 1.82 65º

ZEHAZTASUN HANDIKO MIKROSKOPIO ELEKTRONIKOA (HREM)

Experimental (top) and calculated (bottom) diffraction patterns of a Sr2CuO3 superconductor: left along [001] and right along [110].

SCANING MIKROSKOPIO ELEKTRONIKOA (SEM)

Ile bat

Odol-zelula gorriak

p

hNon de Broglie-ren

uhin luzera den.

...3,2,1 nnvrme

Mekanika kuantikoa ulertu ahal izateko uhinak ulertu behar dire lehenengo!

Uhin geldikorretan:

rn 2

NOLA ULER DAITEKE MOMENTU ANGELUARRAREN KUANTIZAZIOA?

Fourier-en Teorema behar da partikula baten uhina adierazteko

dkekax ikx)()0,(

BI ZIRRIKITUEN SAIAKUNTZA

B. Uhinak

A. Balak (edo golf-pilotak)

Feynman, Leighton eta Sands, Mecánica Cuántica (Física, III alea),

Fondo Educativo Interamericano, 19711ngo kapitulua.

http://www.hqrd.hitachi.co.jp/em/doubleslit.cfm

C. Elektroiak

Elektroiak behatuz

"Suppose we now see what happens when subatomic particles like neutrons are fired towards the two slits (instead of the golf balls). If we place a photographic film across the target then we find the striking result. The neutrons behave like the golf balls in the sense that each hit on the target film produces a definite mark. But as more and more neutrons are fired at the screen the individual hits build up a picture that has the characteristics of a wave interference pattern. There are bands where there is a high development of the target, evenly interspersed with underdeveloped bands each possessing some statistical scatter. Although the neutrons arrive at the target as distinct objects, like the golf balls, the probability that they hit a particular point on the target is determined by a wave intensity. If we close one of the slits then this produces a single wave-intensity distribution with no interference just as in the case with the light-waves. Hence the neutrons manifest particle and wave properties at the same time: they arrive at the target as distinct `hits', but with an intensity pattern characteristic of a wave.

There are further peculiar aspects of the wave interference pattern produced at the target screen by the neutrons, which make it subtler in nature than the 'ordinary' interference pattern produced by the light waves. If we fire the neutrons slowly, one at a time, towards the screen so that we can watch the film developing neutron by neutron, and so avoid any obvious interaction between different neutrons which would lead to interference, then we still find the interference pattern being built up bit by bit. More striking still, we could set up many identical versions of this experiment all over the world and fire just one neutron towards the slits in each of them at a prearranged moment. If we add together the results from all these completely different experiments we would find that the net result would look like the wave interference pattern! The single  neutrons seem to be able to interfere with themselves. This is indeed 'one hand clapping'. We could have arranged for the different experiments to be huge distances apart and synchronized the performance of the different experiments so that in the time that it takes for the neutron to get from its source to the target no signal could travel, even at the speed of tight, between one experiment and another to cause a correlation of their results in some way. The result is the same the individual neutron-hits add to form a correlated interference pattern. How does each neutron know which role to play in order to produce the 'right' big picture of wave interference?

An even more perplexing fact about the microscopic two-slit experiment with the neutrons is that any attempt to unravel the wave-particle ambiguity and discover through which slit a particular neutron actually passed en route to the target invariably destroys the interference pattern seen at the target. Neutrons are rather delicate. If we set up a photoelectric cell at each slit in the screen to be triggered when a neutron passes through that slit, then we might expect to discover through which slit each individual neutron passes on its way to the target. Unfortunately this ambition can never be realized. The intervention of the light from the photoelectric cells alters the behavior of the neutrons in a manner that destroys the wavelike result of the experiment. If we are ever able to determine through which slit a neutron goes, then the pattern seen at the target screen is changed from the light-wave pattern into the particle-like result of the golf balls. Whenever we decide to examine whether a neutron is behaving like a particle and determine through which slit it passes, then, and only then, it is found to behave as a particle. If we do not attempt to determine if it is behaving as a particle, then, and only then, it manifests itself as a wave. It is not possible to construct any device, which can determine through which slit a neutron has passed without destroying the wave interference pattern at the target. 

This is quite unlike anything ever-encountered in classical physics. It confronts all philosophical positions regarding the character of-the laws of Nature and underlying reality with a totally novel challenge. It appears that the observer of the world plays a crucial role in determining what can be observed, but in a way that is subtly different from the old idealist view that everything is in the eye of the beholder. The naive realist would hold to the belief that there is an objective world that exists whether we like it or not, and which possesses definite properties that exist independent of any measurement of them. Unfortunately this does not stand up to its first encounter with the quantum laws of Nature. The observed phenomenon together with the act of observation together determine what can be observed in the two-slit experiment. This does not mean that one should conclude that everything observed is observer-created, in the sense that the idealist or the solipsist might claim. There is no reason to suspend belief in an underlying reality. It is just that the steps we take to establish it determine what it wilt be found to be. Reality is contextual. We must also recognize that, at the very least, this reality which dictates goings-on in the micro-world of photons and neutrons is very different from the approximate impression of it that we have assumed from our contact with large objects whose quantum wavelengths are minute, and whose wave-like properties are for all practical purposes indiscernible. It is not that golf balls do not possess wavelike attributes. They do. But golf balls are so large compared with neutrons and the length of their wave attributes so small, that wave interference effects are indiscernible by the human eye."

John D. Barrow irakaslearen THE WORLD WITHIN THE WORLD liburuan bi fenomenoen

(uhinak eta partikulak) deskribapen interesgarri bat aurki dezakegu:

HEISENBERG-EN ZIURGABETASUNAREN PRINTZIPIOA

W. Heisenberg

Pultsoak (batidoak) aztertzerakoan:

x = /2 = 2/k; x k=2

t =/2 = 2/; t =2

hh

xpx

sin2sin

2

Mikroskopioaren bereizmena (difrakzioa): bi zirrikituen saikuntzan behintzak lehenengo minimoa (d sin =/2)

sartu behar da lentearen barruan (d=x izanik).

Elektroiak behatuz (Heisenberg-en irudizko esperimentua)

Fotoiak, elektroiaren kontra talka egiterakoan,X osagaian jasan dezakeen momentuaren aldaketa

maximoa mikroskopioaren barruan sartzeko.

Max Born(O. Newton-John-en aitona!)

Copenhagen-eko interpretazioa: (http://en.wikipedia.org/wiki/Copenhagen_interpretation)

2

2

d)(1

0

L

L

xxfL

a

FOURIER-EN TRANSFORMAZIOAK

http://www.falstad.com/fourier/index.html

Zein da partikula erlatibista askearenuhinari dagokion ekuazioa?

Ekuazioa lineala delako !

22 )( :batean era beste Edo xxx

)(

)(pA

pa

1)(2

dppa