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basic_tools:hilbert_space [2018/03/28 12:36]
jakobadmin
basic_tools:hilbert_space [2018/05/03 13:23] (current)
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> ​
  
  
-A Hilbert space is the natural arena of quantum mechanics. Each point in this represents one specific configuration a given system can be in. +A Hilbert space is the natural arena of quantum mechanics. Each point in it represents one specific configuration a given system can be in. 
  
  
 <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}}+
  
basic_tools/hilbert_space.1522233394.txt.gz · Last modified: 2018/03/28 10:36 (external edit)