3.1 Basic Concepts and Formulae
135
Hetero-nuclear diatomic molecules such as CO and linear polyatomic molecule
such as HCN, do possess dipolemoment and so also rotational spectrum.
The selection rule is
ΔJ = 0, ±1.
(3.20)
The occurrence of a rotational Raman spectrum depends on the change in polarizibility. Such a change can occur in symmetric top molecules. The selection rule is
ΔJ = 0, ±2.
(3.21)
Required properties of the wave function
Ψ should be finite, single-valued and continuous. These requirements follow from
the interpretation of |ψ|
2 as the probability density.
Ladder operators
Raising operator:
J + | jm >=
( j + m + 1)( j − m)| j, m + 1 >
Lowering operator:
J − | jm >=
( j − m + 1)( j + m)| j, m − 1 >
(3.23)
The Klein–Gordon equation for the relativistic free motion of a spinless particle
of rest mass m.
∇
2
φ −
1
c 2
∂
2
ϕ
∂t 2 =
m
2 c
2
ϕ
2
(3.24)
If the quantum of nuclear field is assumed to have mass m, then its range
R ∼
mc
(3.25)
The variation method
It consists of evaluating the integrals on the RHS of the inequality
E 0
ψ
∗ H ψ dτ
|ψ| 2 dτ
(3.26)