basic_tools:hilbert_space
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basic_tools:hilbert_space [2018/04/09 06:40] ronaldwilliams [Intuitive] |
basic_tools:hilbert_space [2018/04/13 11:24] bogumilvidovic [Concrete] |
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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. | ||
basic_tools/hilbert_space.txt · Last modified: 2018/05/03 13:23 by jakobadmin
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