91影视

$\stackrel{}{c_a=-\frac{i}{2\sout{h}}}{V}_{ab}{e}^{i蝇t}{e}^{-i{蝇}_{0}t}{c}_b;\stackrel{.}{c_b}=-\frac{i}{2\sout{h}}{V}_{ba}{e}^{-i蝇t}{e}^{-i{蝇}_{0}t}{c}_a$

Differentiate the latter, and substitute in the former:

$$\begin{gathered} C_b=-i\frac{V_{ba}}{2\sout{h}}\left[i({蝇}_0-蝇)e^{i({蝇}_0-蝇)t}{c}_a+e^{i({蝇}_0-蝇)t}\stackrel{藱}{c_a}\right] \\ =i({蝇}_0-蝇)\left[-i\frac{V_{ba}}{2\sout{h}}{e}^{i({蝇}_0-蝇)t}{c}_a\right]-i\frac{V_{ab}}{2\sout{h}}{e}^{i({蝇}_0-蝇)t}\left[-i\frac{V_{ab}}{2\sout{h}}{e}^{i({蝇}_0-蝇)t}{c}_b\right]=i({蝇}_0-蝇)\stackrel{藱}{c_b}-\frac{{\left|V_{ab}\right|}^2}{{\left(2\sout{h}\right)}^2}{c}_b. \\ \frac{d^2{c}_b}{d{t}^2}+i(蝇-{蝇}_0)\frac{d{c}_b}{dt}+\frac{{\left|V_{ab}\right|}^2}{{\left(2\sout{h}\right)}^2}{c}_b=0.\mathrm{Soluation}\mathrm{of}\mathrm{the}\mathrm{form}{\mathrm{c}}_{\mathrm{b}}={\mathrm{e}}^{\mathrm{位迟}}:{\mathrm{位}}^2+\mathrm{i}({\mathrm{蝇}}_0-\mathrm{蝇})\mathrm{位}+\frac{{\left|{\mathrm{V}}_{\mathrm{ab}}\right|}^2}{4{\sout{\mathrm{h}}}^2} \\ \mathrm{位}=\frac{1}{2}\left[-\mathrm{i}(\mathrm{蝇}-{\mathrm{蝇}}_0)卤\sqrt{-{(\mathrm{蝇}-{\mathrm{蝇}}_0)}^2-\frac{\left|\mathrm{V}\right|}{}}\right] \end{gathered}$$_ab²h²=i-(蝇-蝇0)2卤蝇r,with蝇r.Generalsoluation:cb(t)=Aei(蝇-蝇0)2+蝇rt+Bei(蝇-蝇0)2+蝇rt=e-i(蝇-蝇0)t/2Aei蝇rt+Be-i蝇rt,or,moreconveniently:cb(t)=e-i(蝇-蝇0)t/2Ccos(蝇rt)+Dsin(蝇rt).Butcb(0)=0soC=0cb(t)=Dei(蝇0-蝇)t/2sin(蝇rt).cb=Di蝇0-蝇2ei(蝇0-蝇)t/2sin藱uncaught exception: Invalid chunk

in file: /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 68
#0 /var/www/html/integration/lib/php/Boot.class.php(769): com_wiris_plugin_impl_HttpImpl_1(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Invalid chunk') #1 /var/www/html/integration/lib/haxe/Http.class.php(532): _hx_lambda->execute('Invalid chunk') #2 /var/www/html/integration/lib/php/Boot.class.php(769): haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Invalid chunk') #3 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(30): _hx_lambda->execute('Invalid chunk') #4 /var/www/html/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Invalid chunk') #5 /var/www/html/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), Object(sys_net_Socket), NULL) #6 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(43): haxe_Http->request(true) #7 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(268): com_wiris_plugin_impl_HttpImpl->request(true) #8 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(307): com_wiris_plugin_impl_RenderImpl->showImage('b21ce702a20675c...', NULL, Object(PhpParamsProvider)) #9 /var/www/html/integration/createimage.php(17): com_wiris_plugin_impl_RenderImpl->createImage('uncaught exception: Invalid chunk

in file: /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 68
#0 /var/www/html/integration/lib/php/Boot.class.php(769): com_wiris_plugin_impl_HttpImpl_1(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Invalid chunk') #1 /var/www/html/integration/lib/haxe/Http.class.php(532): _hx_lambda->execute('Invalid chunk') #2 /var/www/html/integration/lib/php/Boot.class.php(769): haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Invalid chunk') #3 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(30): _hx_lambda->execute('Invalid chunk') #4 /var/www/html/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Invalid chunk') #5 /var/www/html/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), Object(sys_net_Socket), NULL) #6 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(43): haxe_Http->request(true) #7 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(268): com_wiris_plugin_impl_HttpImpl->request(true) #8 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(307): com_wiris_plugin_impl_RenderImpl->showImage('46fca5c470c333f...', NULL, Object(PhpParamsProvider)) #9 /var/www/html/integration/createimage.php(17): com_wiris_plugin_impl_RenderImpl->createImage('

$$\begin{gathered} \mathrm{conveniently}:{\mathrm{c}}_{\mathrm{b}}\left(\mathrm{t}\right)={\mathrm{e}}^{-\mathrm{i}(\mathrm{蝇}-{\mathrm{蝇}}_0)\mathrm{t}/2}\left[\mathrm{C}\cos \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right)+\mathrm{D}\sin \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right)\right].\mathrm{But}{\mathrm{c}}_{\mathrm{b}}\left(0\right)=0\mathrm{so}\mathrm{C}=0 \\ {\mathrm{c}}_{\mathrm{b}}\left(\mathrm{t}\right)={\mathrm{De}}^{\mathrm{i}({\mathrm{蝇}}_0-\mathrm{蝇})\mathrm{t}/2}\sin \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right).\stackrel{藱}{{\mathrm{c}}_{\mathrm{b}}=\mathrm{D}\left[\mathrm{i}\left(\frac{{\mathrm{蝇}}_0-\mathrm{蝇}}{2}\right){\mathrm{e}}^{\mathrm{i}({\mathrm{蝇}}_0-\mathrm{蝇})\mathrm{t}/2}\sin \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right)+{\mathrm{蝇}}_{\mathrm{r}}{\mathrm{e}}^{\mathrm{i}(\mathrm{蝇}-{\mathrm{蝇}}_0)\mathrm{t}/2}\cos \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right)\right]} \\ {\mathrm{c}}_a\left(\mathrm{t}\right)=i\frac{2\sout{h}}{V_{ba}}{e}^{\mathrm{i}({\mathrm{蝇}}_0-\mathrm{蝇})\mathrm{t}}\stackrel{藱}{c_b=}i\frac{2\sout{h}}{V_{ba}}{e}^{\mathrm{i}({\mathrm{蝇}}_0-\mathrm{蝇})\mathrm{t}/2}D\left[\mathrm{i}\left(\frac{{\mathrm{蝇}}_0-\mathrm{蝇}}{2}\right)\sin \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right)+{\mathrm{蝇}}_{\mathrm{r}}\cos \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right)\right].\mathrm{But}{\mathrm{c}}_{\mathrm{a}} \\ 1=\mathrm{i}\frac{2\sout{\mathrm{h}}}{{\mathrm{V}}_{\mathrm{ba}}}{\mathrm{D蝇}}_{\mathrm{r}},\mathrm{or}\mathrm{D}=\frac{-{\mathrm{iV}}_{\mathrm{ba}}}{2\sout{\mathrm{h}}{\mathrm{蝇}}_{\mathrm{r}}} \\ {\mathrm{c}}_{\mathrm{b}}\left(\mathrm{t}\right)=-\frac{\mathrm{i}}{2\sout{\mathrm{h}}{\mathrm{蝇}}_{\mathrm{r}}}{\mathrm{V}}_{\mathrm{ba}}{\mathrm{e}}^{\mathrm{i}({\mathrm{蝇}}_0-\mathrm{蝇})\mathrm{t}/2}\sin \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right),{\mathrm{c}}_{\mathrm{a}}\left(\mathrm{t}\right)={\mathrm{e}}^{\mathrm{i}(\mathrm{蝇}-{\mathrm{蝇}}_0)\mathrm{t}/2}\left[\cos \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right)+\mathrm{i}\left(\frac{{\mathrm{蝇}}_0-\mathrm{蝇}}{2}\right)\sin \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right)\right]. \end{gathered}$$

$$\begin{gathered} C_b=-i\frac{V_{ba}}{2\sout{h}}\left[i({蝇}_0-蝇)e^{i({蝇}_0-蝇)t}{c}_a+e^{i({蝇}_0-蝇)t}\stackrel{藱}{c_a}\right] \\ =i({蝇}_0-蝇)\left[-i\frac{V_{ba}}{2\sout{h}}{e}^{i({蝇}_0-蝇)t}{c}_a\right]-i\frac{V_{ab}}{2\sout{h}}{e}^{i({蝇}_0-蝇)t}\left[-i\frac{V_{ab}}{2\sout{h}}{e}^{i({蝇}_0-蝇)t}{c}_b\right]=i({蝇}_0-蝇)\stackrel{藱}{c_b}-\frac{{\left|V_{ab}\right|}^2}{{\left(2\sout{h}\right)}^2}{c}_b. \\ \frac{d^2{c}_b}{d{t}^2}+i(蝇-{蝇}_0)\frac{d{c}_b}{dt}+\frac{{\left|V_{ab}\right|}^2}{{\left(2\sout{h}\right)}^2}{c}_b=0.\mathrm{Soluation}\mathrm{of}\mathrm{the}\mathrm{form}{\mathrm{c}}_{\mathrm{b}}={\mathrm{e}}^{\mathrm{位迟}}:{\mathrm{位}}^2+\mathrm{i}({\mathrm{蝇}}_0-\mathrm{蝇})\mathrm{位}+\frac{{\left|{\mathrm{V}}_{\mathrm{ab}}\right|}^2}{4{\sout{\mathrm{h}}}^2} \\ \mathrm{位}=\frac{1}{2}\left[-\mathrm{i}(\mathrm{蝇}-{\mathrm{蝇}}_0)卤\sqrt{-{(\mathrm{蝇}-{\mathrm{蝇}}_0)}^2-\frac{{\left|{\mathrm{V}}_{\mathrm{ab}}\right|}^2}{{\sout{\mathrm{h}}}^2}}\right]=\mathrm{i}\left[-\frac{(\mathrm{蝇}-{\mathrm{蝇}}_0)}{2}卤{\mathrm{蝇}}_{\mathrm{r}}\right],\mathrm{with}{\mathrm{蝇}}_{\mathrm{r}}. \\ \mathrm{General}\mathrm{soluation}:{\mathrm{c}}_{\mathrm{b}}\left(\mathrm{t}\right)={\mathrm{Ae}}^{\mathrm{i}\left[\frac{(\mathrm{蝇}-{\mathrm{蝇}}_0)}{2}+{\mathrm{蝇}}_{\mathrm{r}}\right]\mathrm{t}}+{\mathrm{Be}}^{\mathrm{i}\left[\frac{(\mathrm{蝇}-{\mathrm{蝇}}_0)}{2}+{\mathrm{蝇}}_{\mathrm{r}}\right]\mathrm{t}}={\mathrm{e}}^{-\mathrm{i}(\mathrm{蝇}-{\mathrm{蝇}}_0)\mathrm{t}/2}\left[{\mathrm{Ae}}^{{\mathrm{i蝇}}_{\mathrm{r}}\mathrm{t}}+{\mathrm{Be}}^{-{\mathrm{i蝇}}_{\mathrm{r}}\mathrm{t}}\right], \\ \mathrm{or},\mathrm{more} \\ \mathrm{conveniently}:{\mathrm{c}}_{\mathrm{b}}\left(\mathrm{t}\right)={\mathrm{e}}^{-\mathrm{i}(\mathrm{蝇}-{\mathrm{蝇}}_0)\mathrm{t}/2}\left[\mathrm{C}\cos \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right)+\mathrm{D}\sin \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right)\right].\mathrm{But}{\mathrm{c}}_{\mathrm{b}}\left(0\right)=0\mathrm{so}\mathrm{C}=0 \\ {\mathrm{c}}_{\mathrm{b}}\left(\mathrm{t}\right)={\mathrm{De}}^{\mathrm{i}({\mathrm{蝇}}_0-\mathrm{蝇})\mathrm{t}/2}\sin \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right).\stackrel{藱}{{\mathrm{c}}_{\mathrm{b}}=\mathrm{D}\left[\mathrm{i}\left(\frac{{\mathrm{蝇}}_0-\mathrm{蝇}}{2}\right){\mathrm{e}}^{\mathrm{i}({\mathrm{蝇}}_0-\mathrm{蝇})\mathrm{t}/2}\sin \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right)+{\mathrm{蝇}}_{\mathrm{r}}{\mathrm{e}}^{\mathrm{i}(\mathrm{蝇}-{\mathrm{蝇}}_0)\mathrm{t}/2}\cos \left({\mathrm{蝇}}_{\mathrm{r}}\mathrm{t}\right)\right]} \end{gathered}$$uncaught exception: Invalid chunk

in file: /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 68
#0 /var/www/html/integration/lib/php/Boot.class.php(769): com_wiris_plugin_impl_HttpImpl_1(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Invalid chunk') #1 /var/www/html/integration/lib/haxe/Http.class.php(532): _hx_lambda->execute('Invalid chunk') #2 /var/www/html/integration/lib/php/Boot.class.php(769): haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Invalid chunk') #3 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(30): _hx_lambda->execute('Invalid chunk') #4 /var/www/html/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Invalid chunk') #5 /var/www/html/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), Object(sys_net_Socket), NULL) #6 /var/www/html/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(43): haxe_Http->request(true) #7 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(268): com_wiris_plugin_impl_HttpImpl->request(true) #8 /var/www/html/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(307): com_wiris_plugin_impl_RenderImpl->showImage('46fca5c470c333f...', NULL, Object(PhpParamsProvider)) #9 /var/www/html/integration/createimage.php(17): com_wiris_plugin_impl_RenderImpl->createImage('$$\begin{gathered} P_{a鈫�b}\left(t\right)={\left|c_b\left(t\right)\right|}^2={\left(\frac{\left|V_{ab}\right|}{2\sout{h}{蝇}_r}\right)}^2{\sin }^2\left({蝇}_{r}t\right). \\ Thelargestthisgets(whwnsi{n}^2=1whensin2=1)is\frac{{\left|V_{ab}\right|}^2/\sout{h^2}}{4{蝇}_r^2} \\ Andthedenominatorexceedsthenumerator,soP>1(and1onlyif蝇={蝇}_0) \\ {\left|c_a\right|}^2+{\left|c_b\right|}^2={\cos }^2\left({蝇}_{r}t\right)+{\left(\frac{{蝇}_0-蝇}{2{蝇}_r}\right)}^2{\sin }^2\left({蝇}_{r}t\right)+{\left(\frac{\left|V_{ab}\right|}{2h{蝇}_r}\right)}^2{\sin }^2\left({蝇}_{r}t\right). \\ ={\cos }^2\left({蝇}_{r}t\right)+\frac{{(蝇={蝇}_0)}^2+(\left|V\right|}{} \end{gathered}$$_ab/h)²4蝇r2sin2(蝇rt)=cos2(蝇rt)+sin2(蝇rt)=1

If

$$\begin{gathered} {\left|V_{ab}\right|}^2脳\sout{h^2}{(蝇-{蝇}_0)}^2,then{蝇}_r鈮�\frac{1}{2}\left|蝇-{蝇}_0\right|, \\ and{P}_{a鈫�b}鈮�\frac{{\left|V_{ab}\right|}^2}{{\sout{h}}^2}\frac{{\sin }^2\left({\displaystyle \frac{蝇-{蝇}_0}{2}}t\right)}{{(蝇-{蝇}_0)}^2} \\ {P}_{a鈫�b}\left(t\right)={\left|c_b\left(t\right)\right|}^2鈮�\frac{{\left|V_{ab}\right|}^2}{{\sout{h}}^2}\frac{{\sin }^2\left[\left(蝇-{蝇}_0)t/2\right)\right]}{{(蝇-{蝇}_0)}^2} \end{gathered}$$

${蝇}_{r}t=蟺鈬�t=蟺/{蝇}_r.$