Symbole

Superposition: left none mline %psi right rangle als Ket ( Spalten-Vektor )

left langle %psi mline right none

left none mline %psi right rangle

left none mline %psi sup "*" right rangle= a_{1} *left ( stack{1 # 0 # 0} right ) + a_{2}* left ( stack{0 # 1 # 0} right ) a_{3}

stack{ left langle %PHI mline right none left none %psi right rangle = a_{1}c_{1}sup "" + a_{2}c_{2}sup "" + a_{3}c_{3} sup ""

}

stack{ left none mline %psi right rangle

a_{1} *left none mline X right rangle

• a_{2}* left none mline Y right rangle

• a_{3}* left none mline Z right rangle

}

stack{ 
lline  size 15 {%psi} size 20 {x}  size 15 {%psi} rline  =
 left ( stack{
 a_{1}a_{1}sup "*" * a_{1}a_{2}sup "*" * a_{1}a_{3} sup "*" 
 #
  a_{2}a_{1}sup "*" * a_{2}a_{2}sup "*" * a_{2}a_{3} sup "*" 
  # 
  a_{3}a_{1}sup "*" * a_{3}a_{2}sup "*" * a_{3}a_{3} sup "*"
  } right )  
}

stack{ 
(abs{left langle X mline right none left none %psi right rangle}) ^{2} 
= 
a_{1} * a_{ 1 } sup "*" 
}

stack{ 
left none mline %psi  right rangle  =
  
  color aqua {%alpha *  left none mline 0 right rangle  }
  +
  color aqua {%beta  *  left none mline 1 right rangle  }   
}

 abs{%alpha}^2 + abs{%beta}^2 = 1