PhysicsPhysics

Conf. Dr. Radu FecheteConf. Dr. Radu Fechete

Technical University of Cluj-NapocaTechnical University of Cluj-Napoca

Content 1Content 1

Davisson-Germer experimentDavisson-Germer experiment Barrier of potential. Tunnel effectBarrier of potential. Tunnel effect The Hydrogen atomThe Hydrogen atom Quantum numbersQuantum numbers Stern and Gerlach experimentStern and Gerlach experiment Atomic orbitalsAtomic orbitals Atomic spectraAtomic spectra HolographyHolography

Davisson-Germer experimentDavisson-Germer experiment

Barrier of potential. Tunnel effectBarrier of potential. Tunnel effect

l

l

xptU

xptU

xptU

.0

0.0

0.0

tcoefficienontransmissiC

CT

tcoefficienreflexionC

CR

I

III

I

I

2

1,

2

1,

2

1,

2

2,

lEUm2

2

2

2

e1n

n16T

E

EUn

2x

1x

EUm22

eTdx

The Hydrogen atomThe Hydrogen atom

0rUEm2

dz

d

dy

d

dx

d2

e2

2

2

2

2

2

,frR,,r ,f

0rUEm2

sin

1sin

sin

1

rr

rr

12

e2

2

22

2

im212

1n0

mm, ecose

!ml!lnn8

!ml!mln1l2

na

11,,r m

lll

lln, PL

2220

4e

n nh8

emE

12

1nllL

m

m

m2m2

d

d1 PPm

l

Laguerre polynomial Legendre polynomial Quantified energy

Quantum numbersQuantum numbers

im212

1n0

mm, ecose

!ml!lnn8

!ml!mln1l2

na

11,,r m

lll

lln, PL

1 llL

mzLL2me

e

m

2me

L2me

ee

zz

20 Am24-

e

109.27322me

n – principal quantum numbersl – orbital quantum number

m – magnetic quantum number

Bohr magneton

Stern and Gerlach experimentStern and Gerlach experiment

BU

z

B

z

UF

zzz

Energy of a magnetic moment in B

Spin quantum number

2

1zS

Atomic orbitalsAtomic orbitals

Atomic spectraAtomic spectra

Atomic spectraAtomic spectra

1~

~cc

-wave number The theory of quantum transitions

2220

42

8 nh

eZmE en

22

0

4

8 h

eme

2

2

n

ZEn

222 11~

nmZhch

222 11~

nmZH

Rydberg consntant

H= 1.0967758 107 m-1

= 2.15 10-18 J = 13.6 eV

LASERsLASERsDef: light amplification by stimulated emission of radiation

nnmsp,em NAP

uNBP mmnst,abs

m

n

mn

nmmmnnnmst,abssp,em N

N

B

AuuNBNAPP

Tk

E

0nB

n

eNN

Probability of spontaneous emission

Probability of spontaneous absorption

Boltzmann distribution

uNBP nnmstim,em

uNBNAP nnmnnmem

nmTk

h

mn

nmabsem

BeB

AuPP

B

1

18,

3

3

Tk

h

Bec

hTu

Probability of stimulated emission

HolographyHolography

Content 2Content 2

SemiconductorsSemiconductors Hall EffectHall Effect Difference of potential at metal-metal contactDifference of potential at metal-metal contact Thermoelectric effect (Seebeak effect)Thermoelectric effect (Seebeak effect) Magnetic materialsMagnetic materials

DiamagnetismDiamagnetismParamagnetismParamagnetismFerromagnetismFerromagnetismSuperconductivitySuperconductivity

Energetic Bands in solidsEnergetic Bands in solids

Semiconductors:Semiconductors:

Hall EffectHall Effect

a

IBHR

a

IB

ne

1HU

2e

nh

pe

2e

n2h

p

HR

Difference of potential at metal-Difference of potential at metal-metal contactmetal contact

2

1B0102c n

nln

e

Tk

e

LLU

Thermoelectrically effect Thermoelectrically effect (Seebeck effect)(Seebeck effect)

2

1BA n

nlnTT

e

KE

BA TTE

The Peltier effect is considered the inverse of thermoelectric effect consisting in the heat radiation while an electrical current passes through an electical circuit consisting from two different materials: tIbQ

Thermoelectrically effect consist in the apparition of an electromotive tension into a two-metals electrical circuit when a difference of temperature exist between those two contact points.

Magnetic properties of materialsMagnetic properties of materials

mi

N

1iii

N

1ii SIm

M

The total magnetic moment

V

SI

V

m

V

N

1iii

N

1ii

MM

Sample magnetization

Magnetic properties of materialsMagnetic properties of materials

MHB 00

HM m

mr 1

H – magnetic field intensitym – magnetic susceptibilityr – material relative magnetic permeability – material magnetic permeability

r0

Substances classificationSubstances classification

Diamagnetic: (Diamagnetic: (mm < 0 – small; < 0 – small; mm mm(T))(T))

Paramagnetic (Paramagnetic ( mm > 0) > 0)Paramagnetic: (Paramagnetic: ( mm > 0 – small; - Curie law) > 0 – small; - Curie law)

Ferromagnetic (Ferromagnetic ( mm > 0 – large; > 0 – large; mm = = mm(T))(T))AntiferromagneticAntiferromagneticFerrimagnetic.Ferrimagnetic.

Magnetic materials: DiamagnetismMagnetic materials: Diamagnetism

The materials with no permanent magnetic moments are diamagnetic materials. The diamagnetism originates in the change of the electrons orbit in the presence of the external magnetic field.

Paramagnetic materialsParamagnetic materials

T

C Curie law

Ferromagnetic materialsFerromagnetic materials

Ferromagnetic materials are characterized by magnetic memory: Hysteresis curves.

Hc – coercitive fieldsBs – saturation fieldBr – remanent magnetization

Ferromagnetic materialsFerromagnetic materials

Due to the reorientation of elementary magnetic moments the sample magnetization increases with the increase of the external magnetic field.

Barkhausen effect – the increase of magnetization appears in steps.

CT

C

Curie-Weiss

law

Magnetic materialsMagnetic materialsParamagnetic

Ferromagnetic

Antiferromagnetic

Ferrimagnetic

Forcedferromagnetic

SuperconductivitySuperconductivityAn element (inter-metallic alloy, ceramics etc.) that An element (inter-metallic alloy, ceramics etc.) that will conduct electricity below a certain temperature will conduct electricity below a certain temperature without resistance. without resistance.

Superconductor material:Superconductor material:Typical structureTypical structure

Superconductivity : Superconductivity : Meissner effectMeissner effect

The origin of superconductivity The origin of superconductivity Cooper pairsCooper pairs

John Bardeen, Leon Cooper si Robert Schrieffer (BCS theory), after 60 years from the discovery of the supra-conductibility phenomena, assumes that the Cooper pairs are now bosons and are no longer subjected to the Pauli principle of exclusion. The electrons motion inside of superconductor material is perfectly ordered and the interaction with the network is much reduced.

Thank You for your attentionThank You for your attention