Page 127 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

The Electronic System
m
,
θφ)
part are the spherical harmonic functions Y (
(see Table 2.2). The
l
⁄
r
r
radial functions are Rr() = R () r , where the R () follow a dif-
,
,
nl nl
ferential equation of Laguerre type, and are shown in Figure 3.9• for dif-
1

1 1 1 1

5 5

1 1 1

Figure 3.9. The radial wavefunction R () for different and . l
r
n
,
nl
ferent nl,( ) . The wavefunction ψ ( r θφ) (see Table 3.1) has three
,,
,,
nlm
integer parameters:
• n : the quantum number of radial motion,
,
,,
–
• l = 01 … n 1 : the first quantum number of angular motion,
,
,
• m = – 1 … 1 : the second quantum number angular motion
(note that m is an integer, not to be confused with the mass of the
electron).
124 Semiconductors for Micro and Nanosystem Technology