Discussion
The fourth excited state wave function of a one-dimensional infinite square well has.........nodes.
Answer: B
The fourth excited state has four nodes.
In an infinite square well the states are \( \psi_{n} = \sqrt{2/L}\,\sin(n\pi x/L) \), with \( n = 1 \) the ground state. The \( n \)th state has \( n - 1 \) nodes inside the well, not counting the walls where every state vanishes.
The fourth excited state is \( n = 5 \), so it has \( 5 - 1 = 4 \) nodes. Three nodes belong to the third excited state (\( n = 4 \)), and five or six would count the walls or skip a level.
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