Hilbert Space in Quantum Mechanics? Archives - Time Travel, Quantum Entanglement and Quantum Computing https://stationarystates.com/tag/hilbert-space-in-quantum-mechanics/ Not only is the Universe stranger than we think, it is stranger than we can think...Hiesenberg Mon, 03 Jun 2024 14:31:54 +0000 en-US hourly 1 https://wordpress.org/?v=6.6.2 Why Hilbert Space in Quantum Mechanics? https://stationarystates.com/basic-quantum-theory/why-hilbert-space-in-quantum-mechanics/?utm_source=rss&utm_medium=rss&utm_campaign=why-hilbert-space-in-quantum-mechanics Mon, 03 Jun 2024 14:31:54 +0000 https://stationarystates.com/?p=407 Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics – have a common underlying mathematical structure. That common structure is Hilbert space. These two theories are said to be isomorphic. If you […]

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]]> Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics – have a common underlying mathematical structure. That common structure is Hilbert space.

These two theories are said to be isomorphic.

If you assume the space you’re using has a complex inner product, and that it is a complete metric space under that inner product, is what makes it a Hilbert space. SE Wave Mechanics and Matrix Mechanics have this complex inner product and completeness.

 

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