| 41. | Not every wave function belongs to the Hilbert space, though.
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| 42. | Every finite-dimensional inner product space is also a Hilbert space.
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| 43. | Two prominent examples occur for Banach spaces and Hilbert spaces.
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| 44. | This language translates into convergence properties of Hilbert space operators.
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| 45. | Tensor products of Hilbert spaces arise often in quantum mechanics.
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| 46. | Banach spaces are a different generalization of Hilbert spaces.
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| 47. | This is justified rigorously by basic Hilbert space theory.
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| 48. | The Hilbert space describing such a system is two-dimensional.
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| 49. | For separable Hilbert spaces, it is the unique ideal.
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| 50. | For the finite-dimensional complex Hilbert space, one writes
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