The WKB approximation - UNIOS

Contents General remarks The “classical” region

Example: Potential well with no vertical

sin θ1 = sin θ2 =⇒ θ2 = θ1 + nπ =⇒

x2

p(x)dx = n −

x1

Igor Lukaˇcevi´c
The WKB approximation

Tunneling The connection formulas Literature

l walls

⇒
− 1 π , n = 1, 2, 3, . . .

2

UJJS, Dept. of Physics, Osijek

Contents General remarks The “classical” region

Example: Potential well with no vertical

sin θ1 = sin θ2 =⇒ θ2 = θ1 + nπ =⇒

x2

p(x)dx = n −

x1

0, two vertical walls
1/4, one vertical wall

Igor Lukaˇcevi´c
The WKB approximation

Tunneling The connection formulas Literature

l walls

⇒
− 1 π , n = 1, 2, 3, . . .

2

UJJS, Dept. of Physics, Osijek

Contents General remarks The “classical” region

Conclusions

WKB advantages

good for slowly changing w.f.
good for short wavelengths
best in the semi-classical
systems (large n)
one doesn’t even have to solve
the S.E.

Igor Lukaˇcevi´c
The WKB approximation

Tunneling The connection formulas Literature

WKB disadvantages
bad for rapidly changing w.f.
bad for long wavelengths
inappropriate for lower states
(small n)
constraint trade-off (sometimes
not possible)

UJJS, Dept. of Physics, Osijek

Contents General remarks The “classical” region

Contents

1 General remarks
2 The “classical” region
3 Tunneling
4 The connection formulas
5 Literature

Igor Lukaˇcevi´c
The WKB approximation

Tunneling The connection formulas Literature

UJJS, Dept. of Physics, Osijek

Contents General remarks The “classical” region

Literature

1 R. L. Liboff, Introductory Quantum
Francisco, 2003.

2 D. J. Griffiths, Introduction to Qua
Education, Inc., Upper Saddle Rive

3 I. Supek, Teorijska fizika i struktura
Zagreb, 1989.

4 Y. Peleg, R. Pnini, E. Zaarur, Shau
Quantum Mechanics, McGraw-Hill,

Igor Lukaˇcevi´c
The WKB approximation

Tunneling The connection formulas Literature

m Mechanics, Addison Wesley, San
antum Mechanics, 2nd ed., Pearson
er, NJ, 2005.
a materije, II. dio, Sˇkolska knjiga,
um’s Outline of Theory and Problems of
, 1998.

UJJS, Dept. of Physics, Osijek