Re: Forum Tester

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This thread primarily is intended for testing integrity & beta testing of new features......

$\begin{aligned} \Updelta p_\lambda&={\frac{1}{2\Uppsi \epsilon \sqrt{( 2\pi \alpha\beta)^2+\pi(4-8\bar{Q})\alpha\beta+1} \sqrt{ 2\pi \epsilon ^2\alpha\beta- \epsilon ( 2\pi \alpha\beta+1)+\bar{Q}}}}\\ & \quad \times \left[\left\{ \epsilon \left(- 2\pi \epsilon \alpha\beta + 2\pi \alpha\beta-2\bar{Q}+ \epsilon \sqrt{( 2\pi \alpha\beta)^2+\pi (4-8\bar{Q})\alpha\beta+1}\right.\right.\right.\\ &\quad-\left.\left.\left.\sqrt{( 2\pi \alpha\beta)^2+\pi(4-8\bar{Q}) \alpha\beta+1}+ \epsilon +1\right)\pi\right\}\right.\\ &\quad+\left.\left\{ \epsilon \left(- 2\pi \epsilon \alpha\beta+ \epsilon \left( 2\pi \alpha\beta+\sqrt{( 2\pi \alpha\beta)^2+ \pi(4-8\bar{Q})\alpha\beta+1}-1\right)\right.\right.\right.\\ &\quad+\left.\left.\left.2\bar{Q}-\sqrt{( 2\pi \alpha\beta)^2+ \pi(4-8\bar{Q})\alpha\beta+1}-1\right)\pi\right\} \right], \end{aligned} $

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......

$\begin{aligned} \bar{Q}&={\frac{1}{3 \epsilon ^4+24 \epsilon ^2+8}}\left[\vphantom{\left( {\frac{1}{2}}+\alpha \beta \pi \right)^{\frac{1}{2}}}15 { \epsilon }^{3}+8 \epsilon \pi \alpha \beta \left( 4-3 { \epsilon }^{2}-{ \epsilon }^{4} \right)+20 \epsilon \right.\\ & \quad \left.+4\left(\vphantom{\left( {\frac{1}{2}}+\alpha \beta \pi \right)^{\frac{1}{2}}}4 { \epsilon }^{2}{\pi }^{2}{\alpha}^{2}\beta\left( 4-3 { \epsilon }^{2}-{ \epsilon }^{4} \right) ^{2}\right.\right.\\ & \quad \left.\left.+15 \alpha \left( {\frac{4}{3}}+{ \epsilon }^{2} \right){ \epsilon }^{2}\pi \beta \left( 4-3 { \epsilon } ^{2}-{ \epsilon }^{4} \right)-6 \left( \epsilon +1 \right)\left( \epsilon -1 \right)\left(\vphantom{\left( {\frac{1}{2}}+\alpha \beta \pi \right)^{\frac{1}{2}}} { \epsilon }^{8}{\alpha}^{2}{\beta}^{2}{\pi }^{2}\right.\right.\right.\\ & \quad \left.\left.\left.+ \left( {\frac{15}{2}} {\alpha}^ {2}{\beta}^{2}{\pi }^{2}+{\frac{1}{8}}-2 \alpha \beta \pi \right) { \epsilon } ^{6}+\left( -{ \frac{11}{6}} {\alpha}^{2}{\beta}^{2}{\pi }^{2}-{ \frac{33}{2}} \alpha \beta \pi -{\frac{3}{8}}\right ){ \epsilon }^{4}\right.\right.\right.\\ & \quad \left.\left.\left.+\left( -{\frac{16}{3}} {\alpha}^{2}{\beta}^{2}{\pi }^{2}+{ \frac{7}{12}}- {\frac {28}{3}} \alpha \beta \pi \right) { \epsilon }^{2}-{\frac{4}{3}} \left( {\frac{1}{2}}+\alpha \beta \pi \right) ^{2}\right)\right)^{\frac{1}{2}}\right] \epsilon . \end{aligned} $

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......

$\Pi(0,0)=T_{\rm c}^{\,0}\;g^{2}(\alpha)\;\omega_{\rm c}^{-2\alpha}\sum_{n} \int\frac{d^{d}k}{( 2\pi )^{d}}\;\frac{1} {\big( \epsilon _{k}^{2}+\omega_{n}^{2}\big)^{1-\alpha}} $

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This thread primarily is intended for testing integrity & beta testing of new features......

$f_{\vec k}\left(\theta,\varphi\right)=-\lambda\frac{m}{ 2\pi \hbar^2} \\ \left(\left\vert V\left(\vec r\right)\right\vert^{\frac{1}{2}}\varphi_f\left(\vec r\right) \epsilon _V\left(\vec r\right),\left\vert V\left(\vec r\right)\right\vert^{\frac{1}{2}}\psi_{\vec k}^+\left(\vec r\right)\right)\:. $

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......

$g( \epsilon ) = \frac{N} {\sigma \sqrt{ 2\pi }}\exp \left (- \frac{{ \epsilon }^{2}} {2{\sigma }^{2}}\right ),$

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......

$\phi^{({\rm scatt})}_{\alpha}(r,\theta)= \sqrt{\frac{2}{\pi ( \epsilon _{0})^{1/2}k_{0}r}} T_{\alpha}(\theta){\rm exp}\left[ -i \sqrt{ \epsilon _{0}} k_{0}r+ i\pi/4 \right], $

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......

$\begin{aligned} &\left[1+\frac{m\hbar}{2\mu}k_x^2\left(\frac{\Uptheta(\hbar^2k_x^2-2mE)}{\sqrt{\hbar^2k_x^2-2mE}}+\hbox{i}\frac {\Uptheta(2mE-\hbar^2k_x^2)}{\sqrt{2mE-\hbar^2k_x^2}} \right)\right]f(E,k_x,k_y^{\prime})\\ &=-\frac{m}{\mu}\frac{k_x^2}{ 2\pi } \frac{{\hbox{exp}}({\hbox{i}}k^{\prime}_yy_0)}{ k^{\prime2}_y+k_x^2-(2mE/\hbar^2)-\hbox{i} \epsilon }. \end{aligned} $

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......
$
\begin{aligned} q_n&=\left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^n q,\quad Q_n={\frac{2 \epsilon } { \epsilon _\ast+ \epsilon }} \left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^n q,\\ |z|\le L/2:\quad \Upphi=&{\frac{q} {4\pi \epsilon _\ast}} \sum_{n=-\infty}^\infty \left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^{|n|} {\frac{1} {\sqrt{r^2+(z-nL)^2}}},\\ z>L/2:\quad \Upphi=&{\frac{q}{ 2\pi ( \epsilon _\ast+ \epsilon )}} \sum_{n=0}^\infty\left({\frac{ \epsilon _\ast- \epsilon } { \epsilon _\ast+ \epsilon }}\right)^n {\frac{1}{\sqrt{r^2+(z+nL)^2}}}. \end{aligned}$

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......

[Admin]

This thread primarily is intended for testing integrity & beta testing of new features......

[Admin]

$\begin{aligned} &\left(1+\frac{m}{\mu}\frac{k_x^2} { 2\pi }\int\frac{{\hbox{d}}\kappa}{\kappa^2+k_x^2-(2mE/\hbar^2)-\hbox{i} \epsilon } \right)f(E,k_x,k_y^{\prime})\\ &=-\frac{m}{\mu}\frac{k_x^2}{ 2\pi }\frac{{\hbox{exp}}({\hbox{i}}k^{\prime}_yy_0)}{k^{\prime}_y+k_x^2-(2mE/\hbar^2)-{\hbox{i}} \epsilon }. \end{aligned}$

[Admin]

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[Admin]

a test message as always

[Admin]

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[Admin]

$\begin{aligned} \langle k_y|G(E,k_x)|y^{\prime}\rangle=&\frac{1} {\sqrt{ 2\pi }}\int\!{\hbox{d}}k_y^{\prime}\hbox{exp}(-\hbox{i}k^{\prime}_yy^{\prime}) \langle k_y|G(E,k_x)|k_y^{\prime}\rangle\\ = &\frac{1}{\sqrt{ 2\pi }}\frac{1}{k^2_y+k_x^2-(2mE/\hbar^2)-\hbox{i} \epsilon } \left[\hbox{exp}(-\hbox{i}k_yy^{\prime})\right.\\ -&\left.\frac{\hbar k_x^2\ell\Uptheta(\hbar^2k_x^2-2mE)}{ \sqrt{\hbar^2k_x^2-2mE} +\hbar k_x^2\ell}\hbox{exp}\!\left(-\hbox{i}k_y y_0-\sqrt{\hbar^2k_x^2-2mE}\frac{|y^{\prime}-y_0|}{\hbar}\right)\right.\\ -&\left.\hbox{i}\frac{\hbar k_x^2\ell\Uptheta(2mE-\hbar^2k_x^2)}{ \sqrt{2mE-\hbar^2k_x^2}+\hbox{i}\hbar k_x^2\ell} \hbox{exp}\!\left(-\hbox{i}k_y y_0+\hbox{i}\sqrt{2mE-\hbar^2k_x^2} \frac{|y^{\prime}-y_0|}{\hbar}\right)\right]. \end{aligned} $

[Admin]

[doc]src="http://www.scribd.com/embeds/2942002/content?start_page=1&view_mode=list&access_key=key-sxlnrfvqu5s22kzi5xb"[doc]

sdfad

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• kadhadaskdjkadhadaskdjkadhadaskdjkadhadaskdj

[docis]documentId=110829214737-4e3a7b11d0e747048caf9e223bd33f1a[docis]

[Admin]

$\frac{1}{\rho }\frac{{{\text{d}}\rho }}{{{\text{d}}z}} + \frac{1}{w}\frac{{{\text{d}}w}}{{{\text{d}}z}} = - \frac{1}{A}\frac{{{\text{d}}A}}{{{\text{d}}z}},$
[doc]src="http://www.scribd.com/embeds/27438612/content?start_page=1&view_mode=list&access_key=key-2ezi6trbyg08mivwsqdb"[doc]

$z\frac{{{\rm d}^{2} w}}{{{\rm d}z^{2} }} + {\left({1 + 2b - Pr - z} \right)}\frac{{{\rm d}w}}{{{\rm d}z}} - (b - 2)w = 0$

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