ATOMIC PHYSICS Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016 CONTENTS Atomic Physics Particles in 3D Potentials and the Hydrogen Atom Spectral lines of Hydrogen Atom Spectral lines of[.]
Trang 1ATOMIC PHYSICS
Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016
Trang 2CONTENTS
Atomic Physics
Trang 3THE SCHRÖDINGER EQUATION IN THREE DIMENSIONS
ANS : (ii) must be negative
Energy
Potential rgy
KineticEne
2 2
U m
2 E
0 )
U E ( m 2
Trang 4Particle in a Three-Dimensional Box
2
2 2 2 z z
z z
2 2
2
2
2 2 2 y y
Y y
2 2
2
2
2 2 2 x x
x x
2 2
2
x 2 2
2
2 2
2 2
2 2
2
2
2 2
2 2
2 2
2
2 2
2 2
2 2
2
2 2
2 2
2 2
/ iEt
mL 2
n E
) z L
n sin(
L
2 Z
0 Z E m 2 x
Z
mL 2
n E
) y L
n sin(
L
2 Y
0 Y E m 2 x
Y
mL 2
n E
) x L
n sin(
L
2 X
0 X E m 2 x
X
0 E
m 2 x
X X
0 E m 2 z
Z
Z y
Y
Y x
X X
E
) z Z
Z y
Y
Y x
X
X (
m 2
EXYZ
) z
Z XY y
Y XZ x
X YZ ( m 2
) z , y , x ( E
) z
) z , y , x ( y
) z , y , x ( x
) z , y , x ( (
m 2
equation r
Schrodinge
) z ( Z ) y ( Y ) x ( X ) z , y , x (
: Technique Separation
Variable
By
e ) z , y , x ( )
t , z , y , x (
0 z) y, box U(x, the
In
2
2 2 2 z
2 y
2
z
z Y
x 3
mL 2
) n n
n
(
E
) z L
n sin(
) y L
n sin(
) x L
n sin(
L
2 )
z
,
y
,
x
(
Trang 5Energy – level diagram for a particle in
a 3 dimensional cubic box
Having two or more distinct quantum states with the same energy is called degeneracy, and states with the same energy are said
to be degenerate
Trang 6I Electron in moving in the electric field caused by the nucleus, and having the potential energy:
x
è
+
y
z
r
r 4
e )
r (
U
o
2
Schrodinger equation for the electron :
0 ) r (
) r 4
e E
( m 2 ) r (
0 ) r ( )) r ( U E
( m 2 ) r (
o
2 2
2
In the spherical coordinate system, and by the variable separation technique, the wave function has the form:
) , ( Y
) r ( R
) , , r ( )
r ( n , , m
HYDROGEN ATOM
Trang 7) , ( Y
) r ( R
) , , r ( )
r ( n , , m
The wave function describing the state of the electron depends
on 3 quantum numbers n, ℓ ,m
n = 1, 2, 3, … Principal quantum number
ℓ = 0,1, 2…, n-1 Orbital quantum number
m = 0, 1, 2, 3, , ℓ Magnetic quantum number
o o o
a 2 Zr
o
2 / 3
o
1
,
2
a 2 Zr
o
2 / 3
o
0
,
2
a
Zr 2
/ 3
o
0
,
1
e a
Zr a
Z 24
1 R
e a
Zr 2
a
Z 8
1 R
e a
Z 2
R
m 10
53
0 e
m
4 a
cos 8
3 Y
e
sin 8
3 Y
; e
sin 8
3 Y
4
1 Y
10 2
e
2 o o
0 , 1
i 1
, 1
i 1
, 1
0 , 0
Wave function of electron
Yℓm( , ): Spherical harmonics
Rnℓ(r): Laguerre
functions