Question

Formulate an argument explaining why the even wave functions in Fig 10.1 should be lower in energy than their odd partners.

Short answer

The wave function that has more anti-nodes is at a higher energy.

Step-by-step solution

Functions

In the two wells, for each pair of the molecular states, the even function has one less anti-node then their odd partners. When $n=1$the odd function has two anti-nodes and the even function has one distorted anti-node.

Step 2:Relation between energy and wave number

As energy of the particle is proportional to the wave number of its wave function.

Hence, The odd wave function has higher energy and the even function has lower energy or longer wavelength.