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Display information for equation id:math.1618.41 on revision:1618

* Page found: Zustandsvektoren im Hilbertraum (eq math.1618.41)

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TeX (original user input): 

\begin{align}
& \left\langle  \Psi  | \Psi  \right\rangle \ge 0:\left\langle  \Psi  | \Psi  \right\rangle =0\to \left| \Psi  \right\rangle =\left| 0 \right\rangle  \\
& \left\langle  \Psi  | {{\Psi }_{1}}+{{\Psi }_{2}} \right\rangle =\left\langle  \Psi  | {{\Psi }_{1}} \right\rangle +\left\langle  \Psi  | {{\Psi }_{2}} \right\rangle  \\
& \left\langle  {{\Psi }_{1}} | \alpha {{\Psi }_{2}} \right\rangle =\alpha \left\langle  {{\Psi }_{1}} | {{\Psi }_{2}} \right\rangle  \\
& \left\langle  {{\Psi }_{1}} | {{\Psi }_{2}} \right\rangle =\left\langle  {{\Psi }_{2}} | {{\Psi }_{1}} \right\rangle * \\
\end{align}

TeX (checked): 

{\begin{aligned}&\left\langle \Psi |\Psi \right\rangle \geq 0:\left\langle \Psi |\Psi \right\rangle =0\to \left|\Psi \right\rangle =\left|0\right\rangle \\&\left\langle \Psi |{{\Psi }_{1}}+{{\Psi }_{2}}\right\rangle =\left\langle \Psi |{{\Psi }_{1}}\right\rangle +\left\langle \Psi |{{\Psi }_{2}}\right\rangle \\&\left\langle {{\Psi }_{1}}|\alpha {{\Psi }_{2}}\right\rangle =\alpha \left\langle {{\Psi }_{1}}|{{\Psi }_{2}}\right\rangle \\&\left\langle {{\Psi }_{1}}|{{\Psi }_{2}}\right\rangle =\left\langle {{\Psi }_{2}}|{{\Psi }_{1}}\right\rangle *\\\end{aligned}}

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⟨Ψ|Ψ⟩≥0:⟨Ψ|Ψ⟩=0→|Ψ⟩=|0⟩⟨Ψ|Ψ1+Ψ2⟩=⟨Ψ|Ψ1⟩+⟨Ψ|Ψ2⟩⟨Ψ1|αΨ2⟩=α⟨Ψ1|Ψ2⟩⟨Ψ1|Ψ2⟩=⟨Ψ2|Ψ1⟩∗
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Calculated based on the variables occurring on the entire Zustandsvektoren im Hilbertraum page

Identifiers

  • Ψ
  • Ψ
  • Ψ
  • Ψ
  • Ψ
  • Ψ
  • Ψ1
  • Ψ2
  • Ψ
  • Ψ1
  • Ψ
  • Ψ2
  • Ψ1
  • α
  • Ψ2
  • α
  • Ψ1
  • Ψ2
  • Ψ1
  • Ψ2
  • Ψ2
  • Ψ1

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