Use a computer to plot formula directly, as follows. Define z = qA/q, so that (1 – z) = qB/b Then, aside from an overall constant that we’ll ignore, the multiplicity function is [4z(1 – z)]N, where z ranges from 0 to 1 and the factor of 4 ensures that the height of the peak is equal to 1 for any N. Plot this function for N = 1, 10, 100, 1000, and 10,000. Observe how the width of the peak decreases as N increases.

Formula:

Solution to 21P

Step 1</p>

In this question, we need to plot the multiplicity function for N=1,10,100,1000,10000.

Multiplicity function is given by . It is a function of qA, qB and N.

qA and qB are number of energy units

N=Number of oscillators

qA+qB=q

qB=(q-qB)

Solving it we get,

Step 2</p>

Put

So we need to plot the function,

which will give us the gaussian curve.