6.94. Particles of mass m and energy E move from the left to the
potential barrier shown in Fig. 6.3. Find:
(a) the reflection coefficient R of the barrier for E > U 0;
(b) the effective penetration depth of the particles into the region
x > 0 for E < Uo, i.e. the distance from the barrier boundary to
the point at which the probability of finding a particle decreases
e-fold.
t
up
0
Fig. 6.3.
6.95. Employing Eq. (6.2e), find the probability D of an electron
with energy E tunnelling through a potential barrier of width 1
and height U0 provided the barrier is shaped as shown:
(a) in Fig. 6.4;
(b) in Fig. 6.5.
U0
- 1
Fig. 6.4.
Fig. 6.5.
Fig. 6.6.
6.96. Using Eq. (6.2e), find the probability D of a particle of
mass m and energy E tunnelling through the potential barrier
shown in Fig. 6.6, where U (x) = U 0 (1 — x2112).
6.3. PROPERTIES OF ATOMS. SPECTRA
• Spectral labelling of terms: x(L)j, where x = 2S + 1 is the multiplicity, L, S, T are quantum numbers,
L = 0, 1, 2, 3, 4, 5, 6, . . .
(L): S, P, D, F, G, H, I, ...
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