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Quantum Chemistry/Example 3

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Question 3

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Calculate the number of nodes for a particle in a 1D box when n=2 and n=3 when the length of the box is L=5, and give the x-intercept of the node(s).

Wavefunction for a particle in a 1D-Box

Answer

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Part 1

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nnodes=n-1

nnodes=2-1=1

We're looking for one x-intercept.





Use the form where





is the x-intercept

x-intercepts are 0, , 5

0 and 5 are the edges of the box and is the only node.

Part 2

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nnodes=n-1

nnodes=3-1=2

We're looking for two x-intercepts.







x-intercepts are

x-intercepts = 0,

0 and 5 are the edges of the box, and are the nodes.