1000 Solved Problems in Modern Physics

(Romina) #1

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 polar-
izibility. Such a change can occur in symmetric top molecules. The selection rule is


ΔJ= 0 ,± 2. (3.21)

Required properties of the wave function


Ψshould 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 equationfor the relativistic free motion of a spinless particle
of rest massm.


∇^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 massm, 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∗Hψdτ

|ψ|^2 dτ

(3.26)
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