Delta potential scattering - 편집 역사

2021년 2월 17일 (수) 09:30에 Pythagoras0님의 편집

2021-02-17T09:30:58Z

2020년 12월 28일 (월) 12:20에 Pythagoras0님의 편집

2020-12-28T12:20:35Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-28T02:27:56Z

메타데이터: 새 문단

2020년 11월 16일 (월) 15:52에 Pythagoras0님의 편집

2020-11-16T15:52:51Z

2020년 11월 16일 (월) 12:32에 Pythagoras0님의 편집

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2020년 11월 13일 (금) 17:31에 imported>Pythagoras0님의 편집

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imported>Pythagoras0: /* delta potential scattering */

2014-10-06T01:39:45Z

delta potential scattering

imported>Pythagoras0: /* introduction */

2014-10-06T01:29:26Z

introduction

imported>Pythagoras0: /* introduction */

2014-10-06T01:28:36Z

introduction

imported>Pythagoras0: /* introduction */

2014-10-06T01:15:37Z

introduction

@@ 50번째 줄: / 50번째 줄: @@
 [[분류:migrate]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q2381860 Q2381860]

@@ 36번째 줄: / 36번째 줄: @@
 :<math>T=|t|^2=1-R=\cfrac{1}{1+\cfrac{m^2\lambda^2}{\hbar^4k^2}}= \cfrac{1}{1+\cfrac{m \lambda^2}{2\hbar^2 E}}\,\!</math>
-−
 ==계산 리소스==
 * https://docs.google.com/file/d/0B8XXo8Tve1cxZjdDY3BfRFEwM0E/edit
-−
 ==encyclopedia==

← 이전 판		2020년 12월 28일 (월) 02:27 판
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	[[분류:math and physics]]		[[분류:math and physics]]
	[[분류:migrate]]		[[분류:migrate]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q2381860 Q2381860]

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 * [http://en.wikipedia.org/wiki/Delta_potential_barrier_%28QM%29 http://en.wikipedia.org/wiki/Delta_potential_barrier_(QM)]
 [[분류:physics]]
 [[분류:math and physics]]
 [[분류:migrate]]

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 * RHS becomes 0
 :<math>-A_r + A_l + B_r - B_l =\frac{2m\lambda}{ik\hbar^2}(A_r + A_l)</math>
-*  the coefficients $A_r, A_l,B_r,B_l$ must satisfy
+*  the coefficients <math>A_r, A_l,B_r,B_l</math> must satisfy
 :<math>
 \begin{cases}

← 이전 판		2020년 11월 13일 (금) 17:31 판
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	[[분류:math and physics]]		[[분류:math and physics]]
	[[분류:math and physics]]		[[분류:math and physics]]
		+	[[분류:migrate]]

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 * special case of scattering problem <math>A_r=1,  A_l=r,  B_r=t , B_l = 0</math>
-*  wave function<br><math>\psi(x) = \begin{cases} \psi_{\mathrm L}(x) = e^{ikx} + re^{-ikx}, & \text{ if } x<0; \\ \psi_{\mathrm R}(x) =te^{ikx} , & \text{ if } x>0, \end{cases}</math><br>
+*  wave function
 * <math>t-r=1</math>
+:<math>t=\cfrac{1}{1-\cfrac{m\lambda}{i\hbar^2k}}\,\!</math>
-* <math>t-r=1</math><br><math>t=\cfrac{1}{1-\cfrac{m\lambda}{i\hbar^2k}}\,\!</math><br><math>r=\cfrac{1}{\cfrac{i\hbar^2 k}{m\lambda} - 1}\,\!</math><br><math>R=|r|^2=\cfrac{1}{1+\cfrac{\hbar^4k^2}{m^2\lambda^2}}= \cfrac{1}{1+\cfrac{2\hbar^2 E}{m\lambda^2}}.\,\!</math><br><math>T=|t|^2=1-R=\cfrac{1}{1+\cfrac{m^2\lambda^2}{\hbar^4k^2}}= \cfrac{1}{1+\cfrac{m \lambda^2}{2\hbar^2 E}}\,\!</math><br>
+:<math>r=\cfrac{1}{\cfrac{i\hbar^2 k}{m\lambda} - 1}\,\!</math>

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 *  Let the potential is given by
 :<math>V(x) = \lambda\delta(x)</math>
 :<math>\psi(x) = \begin{cases} \psi_{\mathrm L}(x) = A_{\mathrm r}e^{ikx} + A_{\mathrm l}e^{-ikx}, & \text{ if } x<0; \\ \psi_{\mathrm R}(x) = B_{\mathrm r}e^{ikx} + B_{\mathrm l}e^{-ikx}, & \text{ if } x>0, \end{cases}</math>
 *  we impose two conditions on the wave function

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
-*  Let the potential is given by <math>V(x) = \lambda\delta(x)</math><br><math>\psi(x) = \begin{cases} \psi_{\mathrm L}(x) = A_{\mathrm r}e^{ikx} + A_{\mathrm l}e^{-ikx}, & \text{ if } x<0; \\ \psi_{\mathrm R}(x) = B_{\mathrm r}e^{ikx} + B_{\mathrm l}e^{-ikx}, & \text{ if } x>0, \end{cases}</math><br>
+*  Let the potential is given by
-*  we impose two conditions on the wave function<br>
+:<math>V(x) = \lambda\delta(x)</math>
-**  the wave function be continuous in the origin
+:<math>\psi(x) = \begin{cases} \psi_{\mathrm L}(x) = A_{\mathrm r}e^{ikx} + A_{\mathrm l}e^{-ikx}, & \text{ if } x<0; \\ \psi_{\mathrm R}(x) = B_{\mathrm r}e^{ikx} + B_{\mathrm l}e^{-ikx}, & \text{ if } x>0, \end{cases}</math>
-**  integrate the Schrödinger equation around x = 0, over an interval [−ε, +ε] and In the limit as ε → 0, the right-hand side of this equation vanishes; the left-hand side becomes
+*  we impose two conditions on the wave function
-*  first condition<br><math>\psi(0) =\psi_L(0) = \psi_R(0) = A_r + A_l = B_r + B_l</math><br><math>A_r + A_l - B_r - B_l = 0</math><br>
+**  the wave function be continuous in the origin
-*  second condition<br><math> -\frac{\hbar^2}{2 m} \int_{-\epsilon}^{+\epsilon} \psi''(x) \,dx + \int_{-\epsilon}^{+\epsilon} V(x)\psi(x) \,dx = E \int_{-\epsilon}^{+\epsilon} \psi(x) \,dx</math><br> LHS becomes <math>-\frac{\hbar^2}{2m}[\psi_R'(0)-\psi_L'(0)] +\lambda\psi(0)</math><br> RHS becomes 0<br><math>-A_r + A_l + B_r - B_l =\frac{2m\lambda}{ik\hbar^2}(A_r + A_l)</math><br>
+**  integrate the Schrödinger equation around x = 0, over an interval [−ε, +ε] and In the limit as ε → 0, the right-hand side of this equation vanishes; the left-hand side becomes
-*  the coefficient must satisfy<br><math>A_r + A_l - B_r - B_l = 0</math><br><math>-A_r + A_l + B_r - B_l =\frac{2m\lambda}{ik\hbar^2}(A_r + A_l)</math><br>
+*  first condition
+:<math>\psi(0) =\psi_L(0) = \psi_R(0) = A_r + A_l = B_r + B_l</math>
+:<math>A_r + A_l - B_r - B_l = 0</math>
 *  second condition
+:<math> -\frac{\hbar^2}{2 m} \int_{-\epsilon}^{+\epsilon} \psi''(x) \,dx + \int_{-\epsilon}^{+\epsilon} V(x)\psi(x) \,dx = E \int_{-\epsilon}^{+\epsilon} \psi(x) \,dx</math>
 ==delta potential scattering==