Elements of Quantum Theory
83
Tunnelling
voltage
Instrumentation
Control voltages for piezotube
Tunneling
current amplifier
Distance control
and scanning unit
Piezoelectric tube
with electrodes
Tip
Data processing
and display
Fig. 3.3
Fig. 3.4 Image of reconstruction on
Fig. 3.5 An image of single-walled
a clean Gold surface
carbon nanotube
3.8 PARTICLE IN A BOX
An example of a particle in a potential which allows only discrete values for the
energy of the particle is now described.
Consider a particle in a one-dimensional potential which is zero for
0 ≤ x ≤ l, and is infinite for x < 0 or x > l (see Fig. 3.3). The Schrödinger equation
for the particle with well-defined energy is
2
2
2
( )
2
d
x
m dx
φ
−
= Eφ (x), 0 ≤ x ≤ l
(3.95)
whose solutions can be written as
83
Tunnelling
voltage
Instrumentation
Control voltages for piezotube
Tunneling
current amplifier
Distance control
and scanning unit
Piezoelectric tube
with electrodes
Tip
Data processing
and display
Fig. 3.3
Fig. 3.4 Image of reconstruction on
Fig. 3.5 An image of single-walled
a clean Gold surface
carbon nanotube
3.8 PARTICLE IN A BOX
An example of a particle in a potential which allows only discrete values for the
energy of the particle is now described.
Consider a particle in a one-dimensional potential which is zero for
0 ≤ x ≤ l, and is infinite for x < 0 or x > l (see Fig. 3.3). The Schrödinger equation
for the particle with well-defined energy is
2
2
2
( )
2
d
x
m dx
φ
−
= Eφ (x), 0 ≤ x ≤ l
(3.95)
whose solutions can be written as