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equations:schroedinger_equation

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equations:schroedinger_equation [2019/05/21 17:12]
michael Latex footnotes don't work, use docuwiki syntax of `((<footnote>))` instead
equations:schroedinger_equation [2020/04/10 11:40]
109.81.208.52 [Concrete]
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 <tabbox Concrete> ​ <tabbox Concrete> ​
-In the Schrödinger equation, the <color firebrick>​wave-function</​color>​ $\color{firebrick}{\Psi(\vec{x},​t)}$ describes the state of the system. This means concretely that ${ \Psi(\vec{x},​t)}$ encodes, for example, if a given system is excited or in its rest state. The wave-function is a [[basic_tools:​complex_analysis|complex function]], which means that at a given point in space, say $ \vec{x}= (1,4,7)$, and time, say $t=9s$, the wave function is a complex number: ${\Psi(1,​4,​7,​9)}= 5 + 3 i$. The wave-function at a given point in space and time yields a probability amplitude. By taking the absolute square of an probability amplitude we get the probability density and by integrating over some spatial volume we get the probability ​to the the particle within this volume.+In the Schrödinger equation, the <color firebrick>​wave-function</​color>​ $\color{firebrick}{\Psi(\vec{x},​t)}$ describes the state of the system. This means concretely that ${ \Psi(\vec{x},​t)}$ encodes, for example, if a given system is excited or in its rest state. The wave-function is a [[basic_tools:​complex_analysis|complex function]], which means that at a given point in space, say $ \vec{x}= (1,4,7)$, and time, say $t=9s$, the wave function is a complex number: ${\Psi(1,​4,​7,​9)}= 5 + 3 i$. The wave-function at a given point in space and time yields a probability amplitude. By taking the absolute square of an probability amplitude we get the probability density and by integrating over some spatial volume we get the probability ​of the particle ​being within this volume.
  
 The left-hand side of the Schrödinger equation denotes the <color darkturquoise></​color>​ of the wave function. We act with the <color darkturquoise>​partial derivative</​color>​ $\color{darkturquoise}{\partial_t}$ on our wave-function and the result: ${\partial_t}{ \Psi(\vec{x},​t)}$ denotes how the wave function changes as time passes on.  The left-hand side of the Schrödinger equation denotes the <color darkturquoise></​color>​ of the wave function. We act with the <color darkturquoise>​partial derivative</​color>​ $\color{darkturquoise}{\partial_t}$ on our wave-function and the result: ${\partial_t}{ \Psi(\vec{x},​t)}$ denotes how the wave function changes as time passes on. 
equations/schroedinger_equation.txt · Last modified: 2020/11/21 01:43 by 2a01:cb15:33b:c600:f4a9:8015:b3fa:6b19