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Display information for equation id:math.1699.14 on revision:1699

* Page found: Dynamik des 2- Zustands- Systems (eq math.1699.14)

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Dynamik des 2- Zustands- Systems Eq: math.1699.14

Hash: ae84da6c30890745a347409102b81a6e

TeX (original user input):

{{\left| {{\left\langle {{{\hat{\bar{\sigma }}}}_{{}}} \right\rangle }_{t}} \right|}^{2}}={{\left\langle {{{\hat{\bar{\sigma }}}}_{1}} \right\rangle }_{t}}^{2}+{{\left\langle {{{\hat{\bar{\sigma }}}}_{2}} \right\rangle }_{t}}^{2}+{{\left\langle {{{\hat{\bar{\sigma }}}}_{3}} \right\rangle }_{t}}^{2}={{\left\langle {{{\hat{\bar{\sigma }}}}_{1}} \right\rangle }_{0}}^{2}\left[ {{\cos }^{2}}\left( 2{{\omega }_{l}}t \right)+{{\sin }^{2}}\left( 2{{\omega }_{l}}t \right) \right]+{{\left\langle {{{\hat{\bar{\sigma }}}}_{3}} \right\rangle }_{0}}^{2}={{\left\langle {{{\hat{\bar{\sigma }}}}_{1}} \right\rangle }_{0}}^{2}+{{\left\langle {{{\hat{\bar{\sigma }}}}_{3}} \right\rangle }_{0}}^{2}

TeX (checked):

{{\left|{{\left\langle {{\hat {\bar {\sigma }}}_{}}\right\rangle }_{t}}\right|}^{2}}={{\left\langle {{\hat {\bar {\sigma }}}_{1}}\right\rangle }_{t}}^{2}+{{\left\langle {{\hat {\bar {\sigma }}}_{2}}\right\rangle }_{t}}^{2}+{{\left\langle {{\hat {\bar {\sigma }}}_{3}}\right\rangle }_{t}}^{2}={{\left\langle {{\hat {\bar {\sigma }}}_{1}}\right\rangle }_{0}}^{2}\left[{{\cos }^{2}}\left(2{{\omega }_{l}}t\right)+{{\sin }^{2}}\left(2{{\omega }_{l}}t\right)\right]+{{\left\langle {{\hat {\bar {\sigma }}}_{3}}\right\rangle }_{0}}^{2}={{\left\langle {{\hat {\bar {\sigma }}}_{1}}\right\rangle }_{0}}^{2}+{{\left\langle {{\hat {\bar {\sigma }}}_{3}}\right\rangle }_{0}}^{2}

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{| {⟨ {\hat{\bar{σ}}}_{} ⟩}_{t} |}^{2} = {⟨ {\hat{\bar{σ}}}_{1} ⟩}_{t}^{2} + {⟨ {\hat{\bar{σ}}}_{2} ⟩}_{t}^{2} + {⟨ {\hat{\bar{σ}}}_{3} ⟩}_{t}^{2} = {⟨ {\hat{\bar{σ}}}_{1} ⟩}_{0}^{2} [\cos^{2} (2 ω_{l} t) + \sin^{2} (2 ω_{l} t)] + {⟨ {\hat{\bar{σ}}}_{3} ⟩}_{0}^{2} = {⟨ {\hat{\bar{σ}}}_{1} ⟩}_{0}^{2} + {⟨ {\hat{\bar{σ}}}_{3} ⟩}_{0}^{2}

<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mover><mover><mi>σ</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><msup><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mover><mover><mi>σ</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><msup><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mover><mover><mi>σ</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><msup><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mover><mover><mi>σ</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><msup><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mover><mover><mi>σ</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mi>cos</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">+</mo><msup><mi>sin</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo stretchy="false">+</mo><msup><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mover><mover><mi>σ</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><msup><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mover><mover><mi>σ</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><msup><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mover><mover><mi>σ</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mstyle></mrow></math>

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Identifiers

${\hat{\bar{σ}}}_{t}$

${\hat{\bar{σ}}}_{1}_{t}$

${\hat{\bar{σ}}}_{2}_{t}$

${\hat{\bar{σ}}}_{3}_{t}$

${\hat{\bar{σ}}}_{1}_{0}$

$ω_{l}$

$t$

$ω_{l}$

$t$

${\hat{\bar{σ}}}_{3}_{0}$

${\hat{\bar{σ}}}_{1}_{0}$

${\hat{\bar{σ}}}_{3}_{0}$

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