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Why do symmetric wave function has less energy than the anti symmetric wave function and how does it connect to the number of the nodes (why existence of a node point in the anti symmetric tells us that this is more energetic function?)

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- Thread starter Cosmossos
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Why do symmetric wave function has less energy than the anti symmetric wave function and how does it connect to the number of the nodes (why existence of a node point in the anti symmetric tells us that this is more energetic function?)

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Simon Bridge

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An even number of nodes means there is an antinode at the middle of the potential - so there is a relatively higher probability of finding the particle, in that state, close to the center, which makes it more "tight" - the particle spends more time hanging around the middle away from the edges. This makes it harder to pull away, therefore, lower energy.

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