Editing Klein Gordon und Relativität
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Latest revision | Your text | ||
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{{NumBlk|:| | {{NumBlk|:| | ||
<math>\left( \begin{align} | |||
& {{x}'} \\ | & {{x}'} \\ | ||
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mit | mit | ||
<math>\beta =\frac{v}{c}\quad \gamma =\frac{1}{\sqrt{1-{{\beta }^{2}}}}</math> | |||
Daraus folgt (mit v → -v) <font color="#3399FF">'''''(CHECK)'''''</FONT> | Daraus folgt (mit v → -v) <font color="#3399FF">'''''(CHECK)'''''</FONT> | ||
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{{NumBlk|:| | {{NumBlk|:| | ||
<math>\left( \begin{align} | |||
& x \\ | & x \\ | ||
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Wir überprüfen die Übereinstimmung mit (1.10) | Wir überprüfen die Übereinstimmung mit (1.10) | ||
<math>\begin{align} | |||
& \underline{{{{{x}'}}^{2}}-{{c}^{2}}{{{{t}'}}^{2}}}=\left( \begin{matrix} | & \underline{{{{{x}'}}^{2}}-{{c}^{2}}{{{{t}'}}^{2}}}=\left( \begin{matrix} | ||
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Hierzu | Hierzu | ||
<math>\begin{align} | |||
& {{\partial }_{x}}={{\partial }_{x}}\left( {{x}'} \right){{\partial }_{{{x}'}}}+{{\partial }_{x}}\left( {{t}'} \right){{\partial }_{{{t}'}}}=\gamma \,{{\partial }_{{{x}'}}}-\frac{\gamma \beta }{c}{{\partial }_{{{t}'}}} \\ | & {{\partial }_{x}}={{\partial }_{x}}\left( {{x}'} \right){{\partial }_{{{x}'}}}+{{\partial }_{x}}\left( {{t}'} \right){{\partial }_{{{t}'}}}=\gamma \,{{\partial }_{{{x}'}}}-\frac{\gamma \beta }{c}{{\partial }_{{{t}'}}} \\ | ||
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{{NumBlk|:| | {{NumBlk|:| | ||
<math>\Psi \left( \underline{x},t \right)={{e}^{\mp \frac{\mathfrak{i} }{\hbar }\sqrt{{{m}^{2}}{{c}^{4}}+{{p}^{2}}{{c}^{2}}}\,t+i\underline{p}.\underline{x}}}</math> | |||
: |(1.14)|RawN=.}} | : |(1.14)|RawN=.}} | ||
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mit | mit | ||
<math>\begin{align} | |||
& -:\,\text{ negative Energie +}\sqrt{{}} \\ | & -:\,\text{ negative Energie +}\sqrt{{}} \\ |