"Quantum scattering"의 두 판 사이의 차이

2013년 2월 19일 (화) 14:39 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} represents a wave traveling to the right, and e^{−ikx} one traveling to the left
e^{−ikx} is incoming wave from the right to the left
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

\(|r|^2+|t|^2=1\)

@@ 12번째 줄: / 12번째 줄: @@
 ==time independent Schrodinger equation==
-* [[Schrodinger equation]]<br><math>E \psi = -\frac{\hbar^2}{2m}{\partial^2 \psi \over \partial x^2} + V(x)\psi</math><br>
+* [[Schrodinger equation]]
-*  simplified form<br><math>-\varphi_{xx}+u(x)\varphi = \lambda\varphi</math><br><math>\varphi_{xx}+(\lambda-u(x))\varphi=0</math><br>
+:<math>E \psi = -\frac{\hbar^2}{2m}{\partial^2 \psi \over \partial x^2} + V(x)\psi</math>
+* simplified form
+:<math>-\varphi_{xx}+u(x)\varphi = \lambda\varphi</math>
+:<math>\varphi_{xx}+(\lambda-u(x))\varphi=0</math>