| 1. | The eigenstates have a physical meaning further than an orthonormal basis.
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| 2. | Applying Gram-Schmidt one obtains an orthonormal basis for.
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| 3. | There is an orthonormal basis of consisting of eigenvectors of.
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| 4. | Every orthonormal basis in a separable Hilbert space is a Schauder basis.
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| 5. | For the last, you typically pick an orthonormal basis.
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| 6. | Thus an orthonormal basis can be chosen on each eigenspace so that:
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| 7. | The columns in are orthonormal and can be extended to an orthonormal basis.
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| 8. | These orbitals form an orthonormal basis for the wave function of the electron.
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| 9. | This is equivalent to the assertion that every Hilbert space has an orthonormal basis.
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| 10. | A basis for consisting of mutually orthogonal unit vectors is called an orthonormal basis.
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