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Quantum Chemistry/Example 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 : 6 1 black white
Answer
Part 1
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
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.