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basic_tools:hilbert_space [2017/11/17 08:44]
162.158.93.60 [Student]
basic_tools:hilbert_space [2018/05/03 13:23] (current)
jakobadmin
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 ====== Hilbert Space ====== ====== Hilbert Space ======
  
-<tabbox Why is it interesting?> ​+//see also [[basic_tools:​configuration_space|Configuration Space]] and [[basic_tools:​phase_space|Phase space]]//
  
-<blockquote>Recall that in Chapter 5 the concept of [[basic_tools:​phase_space|phase space]] was introduced for the +<tabbox Intuitive
-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 +
-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.+
  
-<​cite>​page 257 in "The Emperors new Mind" by R. Penrose</​cite></​blockquote>​ 
  
-**Important Related Concepts:**+A Hilbert space is the natural arena of quantum mechanics. Each point in it represents one specific configuration a given system can be in. 
  
  
-  * [[basic_tools:​phase_space]] +<tabbox Concrete> ​ 
-  [[basic_tools:​configuration_space]] +**Recommended Resources**
-  ​[[theories:​quantum_theory]]+
  
-<tabbox Layman>  +  ​* 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
- +
-<note tip> +
-Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party. +
-</​note>​ +
-   +
-<tabbox Student>  +
-* 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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   ​   ​
-<​tabbox ​Researcher+<​tabbox ​Abstract
  
 <note tip> <note tip>
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 </​note>​ </​note>​
  
---Common Question 1#+<tabbox Why is it interesting?​
  
-  +<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 
 +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 
 +point of Hilbert space now represents the quantum state of an entire system.
  
---Common Question 2#+<​cite>​page 257 in "The Emperors new Mind" by R. Penrose</​cite></​blockquote>
  
-  
-<-- 
-  ​ 
-<tabbox Examples> ​ 
  
---Example1#+</tabbox>
  
-  
-<-- 
- 
---> Example2:# 
- 
-  
-<-- 
-  ​ 
-<tabbox History> ​ 
- 
-</​tabbox>​ 
  
  
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