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basic_tools:hilbert_space [2018/04/09 06:40] ronaldwilliams [Intuitive] |
basic_tools:hilbert_space [2018/05/03 13:23] jakobadmin |
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====== Hilbert Space ====== | ====== Hilbert Space ====== | ||
+ | //see also [[basic_tools:configuration_space|Configuration Space]] and [[basic_tools:phase_space|Phase space]]// | ||
<tabbox Intuitive> | <tabbox Intuitive> | ||
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<tabbox Concrete> | <tabbox Concrete> | ||
+ | **Recommended Resources** | ||
+ | |||
* The best introduction can be found in [[https://www.google.de/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0ahUKEwiR2N7ajcXXAhVMPxoKHQlcAHMQFggtMAE&url=http%3A%2F%2Fwww.springer.com%2Fcda%2Fcontent%2Fdocument%2Fcda_downloaddocument%2F9783319587318-c2.pdf%3FSGWID%3D0-0-45-1610032-p180855298&usg=AOvVaw3e2e_1g_oXSm4c0aqbzyOV|chapter 2 of Twenty-First Century Quantum Mechanics: Hilbert Space to Quantum Computers]] by G. Fano and S. M. Blinder | * The best introduction can be found in [[https://www.google.de/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0ahUKEwiR2N7ajcXXAhVMPxoKHQlcAHMQFggtMAE&url=http%3A%2F%2Fwww.springer.com%2Fcda%2Fcontent%2Fdocument%2Fcda_downloaddocument%2F9783319587318-c2.pdf%3FSGWID%3D0-0-45-1610032-p180855298&usg=AOvVaw3e2e_1g_oXSm4c0aqbzyOV|chapter 2 of Twenty-First Century Quantum Mechanics: Hilbert Space to Quantum Computers]] by G. Fano and S. M. Blinder | ||
* See the nice explanations at page 257ff in "The Emperors new Mind" by R. Penrose | * See the nice explanations at page 257ff in "The Emperors new Mind" by R. Penrose | ||
+ | ---- | ||
<blockquote>The most fundamental property of a Hilbert space is that it is what is called | <blockquote>The most fundamental property of a Hilbert space is that it is what is called | ||
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<blockquote>Recall that in Chapter 5 the concept of [[basic_tools:phase_space|phase space]] was introduced for the | <blockquote>Recall that in Chapter 5 the concept of [[basic_tools:phase_space|phase space]] was introduced for the | ||
description of a classical system. A single point of phase space would be used | description of a classical system. A single point of phase space would be used | ||
- | to represent the (classical) state of an entire physical system. In the [[theories:quantum_theory|quantum | + | to represent the (classical) state of an entire physical system. In the quantum |
- | theory]], the appropriate analogous concept is that of a Hilbert space. A single | + | theory, the appropriate analogous concept is that of a Hilbert space. A single |
point of Hilbert space now represents the quantum state of an entire system. | point of Hilbert space now represents the quantum state of an entire system. | ||
<cite>page 257 in "The Emperors new Mind" by R. Penrose</cite></blockquote> | <cite>page 257 in "The Emperors new Mind" by R. Penrose</cite></blockquote> | ||
- | |||
</tabbox> | </tabbox> | ||
- | {{tag>theories:quantum_theory:quantum_mechanics theories:quantum_theory:quantum_field_theory}} | + | |