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# SI Units of wavefunction

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What are the SI units of the wavefunction Ψ(x).I know that [Ψ(x)]^2 describes the probabilty of finding a quantum object at a certain quantum state but what about the wavefunction instead?

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There is no one answer. The dimensions are inferred from the fact that $\left| \psi\right|^2$ represents a probability density. Perhaps the most straight-forward way is to consider the normalization condition, i.e. that the integral of the probability density over the state space equals a probability of one. As you know, probabilities are dimensionless by definition. If the wave function is represented in $d$ spatial dimensions, the dimension of the wave function thus becomes becomes $\left[ \psi \right]=L^{-d/2}$, where $L$ represents length (the SI unit for which is the metre). You can similarly work out the units for wave functions represented in momentum space.