Physics
Conf. Dr. Radu Fechete
Technical University of Cluj-Napoca
Content 1
Davisson-Germer experiment
 Barrier of potential. Tunnel effect
 The Hydrogen atom
 Quantum numbers
 Stern and Gerlach experiment
 Atomic orbitals
 Atomic spectra
 Holography

Davisson-Germer experiment
Barrier of potential. Tunnel effect
U  0

U  0
U  0

T
2
16n
e
2
n  1

2
2 m  U  E l

UE
n
E

R 




T 

2
C III ,1
C I ,1
pt. 0  x  l
pt. x  l
2
CI ,2
C I ,1
pt. x  0
reflexion coefficient
2
2
Te
transmissi on coefficient
2 2m


x2

x1
 U  E dx
The Hydrogen atom

d 2  d 2  d 2  2m e
 2  2  2 E  Ur   0
2
dx
dy
dz

1
r2
   2  

1  
 
1  2   2m e


r

sin



E

U
r   0





2
2 
2

r

r
sin







 sin    
 
r, ,   Rr  f ,  f ,    
n,l , m r, ,    1
m
2l 1
n l 1
L

Laguerre polynomial


 1  2l  1n  l  m !l  m ! 2l 1


Ln l 1 l e 2 Pl m cos e im
 na 0  8nn  l!l  m !

Pl   1  
m

2 m2
dm m
P 
m
d
Legendre polynomial
mee4
En   2 2 2
8 0 h n
Quantified energy
Quantum numbers
n,l , m r, ,    1
m


 1  2l  1n  l  m !l  m ! 2l 1
l


Ln l 1  e 2 Pl m cos e im
 na 0  8nn  l!l  m !
n – principal quantum numbers
l – orbital quantum number
L   l l  1
m – magnetic quantum number

e 

L
2m e
e
e
z 
Lz 
m
2m e
2m e
e
0 
 9.2732  10 - 24 Am 2
2m e
Lz  m
Bohr magneton
Stern and Gerlach experiment
Bz
U
Fz  
  z
z
z

U  B
Energy of a magnetic moment in B
Spin quantum number
1
Sz   
2
Atomic orbitals
Atomic spectra
Atomic spectra
1
~


-wave number
me Z 2 e 4
En   2 2 2
8 0 h n
The theory of quantum transitions
c
   c~


me e 4
 2 2
8 0 h
Rydberg consntant
Z2
En   2
n
H= 1.0967758 
107
1 
 1
~
  H Z 2  2  2 
n 
m
m-1
 = 2.15 
10-18
J = 13.6 eV
1 
 1
h  hc~
  Z 2  2  2 
n 
m
LASERs
Def: light amplification by stimulated emission of radiation
Boltzmann distribution
Pem ,sp  A nm N n
Probability of
spontaneous emission
Pabs,st  B mn N m u 
Probability of
spontaneous absorption
Pem ,sp  Pabs,st
N n  N0e
Pem ,stim  B nm N n u 
 u 
A nm N n
B mn N m
En
k BT
Probability of
stimulated emission
Pem  A nm N n  Bnm N n u 
Pem  Pabs

 A nm N n  B mn N m u 
A nm
 u 
Bmn e
h
k BT
 Bnm
8h 3
u  , T  
c3
1
e
h
k BT
1
Holography
Content 2
Semiconductors
 Hall Effect
 Difference of potential at metal-metal contact
 Thermoelectric effect (Seebeak effect)
 Magnetic materials

 Diamagnetism
 Paramagnetism
 Ferromagnetism
 Superconductivity
Energetic Bands in solids
Semiconductors:
Hall Effect
1 IB
IB
UH 
 RH
ne a
a
p 2  n 2
h
e
RH 
e p  n 2
h
e


Difference of potential at metalmetal contact
L02  L01 k BT
n1
Uc 

 ln
e
e
n2
Thermoelectrically effect
(Seebeck effect)
n1
K
E   TA  TB   ln
e
n2
E  TA  TB 
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.
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: Q  b  I  t
Magnetic properties of materials
mi
N
N



M   m i   IiSi
i 1
i 1
The total magnetic moment

 M
M

V

m
 i
N
i1
V

 IiSi
N

i1
V
Sample magnetization
Magnetic properties of materials



B  0 H  0 M


M  m  H
 r  1  m
   0 r
H – magnetic field intensity
m – magnetic susceptibility
r – material relative magnetic permeability
 – material magnetic permeability
Substances classification
Diamagnetic: (m < 0 – small; m  m(T))
 Paramagnetic ( m > 0)

Paramagnetic: ( m > 0 – small; - Curie law)
 Ferromagnetic ( m > 0 – large;  m =  m(T))

 Antiferromagnetic
 Ferrimagnetic.
Magnetic 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 materials
C

T
Curie law
Ferromagnetic materials
Ferromagnetic materials are
characterized by magnetic
memory: Hysteresis curves.
Hc – coercitive fields
Bs – saturation field
Br – remanent magnetization
Ferromagnetic 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.
C

T  C
Curie-Weiss
law
Magnetic materials
Paramagnetic
Ferromagnetic
Antiferromagnetic
Ferrimagnetic
Forced
ferromagnetic
Superconductivity
An element (inter-metallic alloy, ceramics etc.) that
will conduct electricity below a certain temperature
without resistance.
Superconductor material:
Typical structure
Superconductivity :
Meissner effect
The origin of superconductivity
Cooper 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 attention