H. Frauenfelder, E. M. Henley, Teilchen und Kerne: Die Welt der subatomaren Physik, S. 428

P. A. Tipler, R. A. Llewellyn, Modern Physics, Fifth Edition S. 605

K. Bethge, U. E. Schröder, Elementarteilchen und ihre Wechselwirkungen, S. 10

H. Frauenfelder, E. M. Henley, Teilchen und Kerne: Die Welt der subatomaren Physik, S. 2

3PlanckGL

c

H. Frauenfelder, E. M. Henley, Teilchen und Kerne: Die Welt der subatomaren Physik, S. 2

528~ 10Planck

cE eVG

10-10

1K

K. Bethge, G. Walter, B. Wiedemann, Kernphysik – Eine Einführung, S. 216

H. Frauenfelder, E. M. Henley, Teilchen und Kerne: Die Welt der subatomaren Physik, S. 514

K. Stierstadt, Physik der Materie, S. 9

Quanten - Korrelationen

1 2 1 1 2 2

2 2 21 2 1 1 2 2

,

,

r r r r

r r r r

1 2 1 1 2 2 1,r r r r r

21 12

links rechts

,

Wsk Wsk

Wsk Wsk W kr rr rs

unkorreliert

1

2

3

z. B.

Korrelation der Wskamplitude( kann integrieren ! )

klassische Korrelation

Fermionen Bosonen

1 2 2 1, ,r r r r 1 2 2 1, ,r r r r

3 512 2 2, , ,S 0,1, 2,S

1 1 1 1

1 1

, ,

, 0

r r r r

r r

1 1, 0r r

0, , , , ,ee p n

3 6 53, ,He Li Cr

, , ,Photon W Z

4 87 52, , , ,H He Rb Cr

60 2,C O

Vertauschung

halbzahlig ganzzahlig

Pauli - Prinzip

( Durchdringenerlaubt )

G. Otter, R. Honecker, Atome – Moleküle – Kerne: Band II, Molekül- und Kernphysik, S. 377

P. A. Tipler, R. A. Llewellyn, Modern Physics, Fifth Edition S. 589

Geometric Requirements of Electron Spin. Electrons cannot spin separately from the space of which they are structured and connected. If they spin freely as discrete particles, the connected space would twist itself up; that is, the coordinate lines of space would stretch and wrap around one another. The structure of space would be torn or ripped; or, one part of space must slide past another section of space. This concept is illogical and meaningless. This is why spin is purely a quantum wave property of matter.

Quarks, leptons & gauge fields By Kerson Huang

Rauch et. al.: Z. Physik B 29, 281-284 (1978)

Fermionen Bosonen

!(!r1,!r2) = !!(!r2,!r1) !(!r1,!r2) = +!(!r2,!r1)

S =12,32,52, ... S = 0, 1, 2, 3, ...

!(!r1,!r1) = 0 !(!r1,!r1) != 0

e!, p+, n, µ, ...3He,6 Li,53 Cr

Photon,W±, Z, ...4He,7 Li,52 Cr

Atoms as waves

1 nK

temperature wavelength

1000 K1 K1 mK1 µK

Room temperature 0.15 10-10 m

Dilution fridgeL He

Laser coolingEvaporative cooling

4.5 10-10 m1.5 10-8 m4.5 10-7 m15 µm

mvh

dB=λ

~ atom

ic siz

e

~ light

wavele

ngth

Cornell Ketterle Wieman

Nobelpreis 2001

BEC

Distinguishable T shirts

Non degenerate states for 3 distinguishable T shirts in 3 shelfs

3! permutations

degenerate state for 3 distinguishable T shirts in lowest shelf

Indistinguishable T shirts

Non degenerate states for 3 indistinguishable T shirts in 3 shelfs

degenerate state for 3 indistinguishable T shirts in lowest shelf

Indistinguishibility reduces number of non-degeneratestates and increases weight of degenerate ones by N!

Effect only important if # non-deg. states is comparable or smaller than N!

M quantum states and N particles M!/(M-N)! non-deg. states

If M ~N non deg states ~N! BEC

Phase space density ~1