"Quantum scattering"의 두 판 사이의 차이

2014년 10월 5일 (일) 20:32 판

\[E \psi = -\frac{\hbar^2}{2m}{\partial^2 \psi \over \partial x^2} + V(x)\psi\]

\[-\varphi_{xx}+u(x)\varphi = \lambda\varphi\] \[\varphi_{xx}+(\lambda-u(x))\varphi=0\]

$e^{−ikx}$ is incoming wave from the right to the left
$e^{ikx}$ represents a wave traveling to the right
reflection and transmission coefficient
- $\varphi \sim e^{-ikx}+\rho(k,t)e^{ikx}$ as $x\to +\infty$
- $\varphi \sim \tau(k,t)e^{-ikx}$ as $x\to -\infty$
$\rho(k,t)$ and $\tau(k,t)$ are called the reflection and transmission coefficient

$r=t-1$

If t is of the form $t=\frac{1}{1-ai}$ (real number a), then

$|r|^2+|t|^2=1$

@@ 18번째 줄: / 18번째 줄: @@
 ==continuous spectrum==
+* $e^{−ikx}$ is incoming wave from the right to the left
-* e^{ikx} represents a wave traveling to the right, and e^{−ikx} one traveling to the left
+* $e^{ikx}$ represents a wave traveling to the right
-* e^{−ikx} is incoming wave from the right to the left
+* reflection and transmission coefficient
-*  reflection and transmission coefficient<br><math>\varphi \sim e^{-ikx}+\rho(k,t)e^{ikx}</math> as <math>x\to +\infty</math><br><math>\varphi \sim \tau(k,t)e^{-ikx}</math> as <math>x\to -\infty</math><br><math>\rho(k,t)</math> and <math>\tau(k,t)</math> are called the reflection and transmission coefficient<br>
+** <math>\varphi \sim e^{-ikx}+\rho(k,t)e^{ikx}</math> as <math>x\to +\infty</math>
+** <math>\varphi \sim \tau(k,t)e^{-ikx}</math> as <math>x\to -\infty</math>
+* <math>\rho(k,t)</math> and <math>\tau(k,t)</math> are called the reflection and transmission coefficient