Formula Sheet - Revision history

Tom Neiser: Reverted edits by Tom Neiser (talk) to last revision by Andy

2021-06-21T13:32:26Z

Reverted edits by Tom Neiser (talk) to last revision by Andy

2021-06-21T13:31:28Z

‎QM

2019-07-24T19:35:34Z

2017-08-18T20:33:04Z

‎EM

2017-04-05T22:22:52Z

2014-07-12T19:49:15Z

‎QM

2014-07-12T19:44:48Z

‎QM

2014-04-14T23:09:55Z

‎CM

2014-04-14T23:09:40Z

‎CM

2014-04-14T23:09:21Z

‎StM

@@ Line 1: / Line 1: @@
 Here is a list of important equations that have been empirically found to be tested in UCLA's comprehensive exams. Feel free to add further equations for good practice (often, an equation can be copied from the corresponding open source wikipedia article). You may also link to good articles on Wikipedia or upload your own questions and solutions.
-<!-- <div class="fb-share-button" data-href="http://developers.facebook.com/docs/plugins/" data-type="button_count"></div>-->
+<div class="fb-share-button" data-href="http://developers.facebook.com/docs/plugins/" data-type="button_count"></div>
@@ Line 21: / Line 21: @@
 Hermitian Operator Properties<div class="mw-collapsible mw-collapsed" style="width:750px">
+  \[
-:<math>
+H^\dagger = H \]\[ \langle a| H |b\rangle = \langle a | H^\dagger |b \rangle\]\[
-H^\dagger = H  \langle a| H |b\rangle = \langle a | H^\dagger |b \rangle
+H = \sum_0^\infty \lambda_n |n \rangle \langle n|= \text{diagonalized}\]
-H = \sum_0^\infty \lambda_n |n \rangle \langle n|= \text{diagonalized}
+   </div>
-</math>
 </div>
 Define degeneracy of observable matrices vs. nondegeneracy:

@@ Line 21: / Line 21: @@
 Hermitian Operator Properties<div class="mw-collapsible mw-collapsed" style="width:750px">
-  \[
-H^\dagger = H \]\[ \langle a| H |b\rangle = \langle a | H^\dagger |b \rangle\]\[
+:<math>
-H = \sum_0^\infty \lambda_n |n \rangle \langle n|= \text{diagonalized}\]
+H^\dagger = H  \langle a| H |b\rangle = \langle a | H^\dagger |b \rangle
-   </div>
+H = \sum_0^\infty \lambda_n |n \rangle \langle n|= \text{diagonalized}
 Define degeneracy of observable matrices vs. nondegeneracy:

← Older revision		Revision as of 19:35, 24 July 2019
Line 1:		Line 1:
	Here is a list of important equations that have been empirically found to be tested in UCLA's comprehensive exams. Feel free to add further equations for good practice (often, an equation can be copied from the corresponding open source wikipedia article). You may also link to good articles on Wikipedia or upload your own questions and solutions.		Here is a list of important equations that have been empirically found to be tested in UCLA's comprehensive exams. Feel free to add further equations for good practice (often, an equation can be copied from the corresponding open source wikipedia article). You may also link to good articles on Wikipedia or upload your own questions and solutions.

−	<div class="fb-share-button" data-href="http://developers.facebook.com/docs/plugins/" data-type="button_count"></div>	+	<!-- <div class="fb-share-button" data-href="http://developers.facebook.com/docs/plugins/" data-type="button_count"></div>-->

@@ Line 406: / Line 406: @@
    \[
 \frac{\partial u}{\partial t} + \nabla\cdot\mathbf{S} = - \mathbf{J}\cdot\mathbf{E},
-where '''J''' is the ''total'' current density and the energy density ''u'' is
+where  '''J'''  is the ''total'' current density and the energy density ''u'' is
 u = \frac{1}{2}\left(\varepsilon_0 \mathbf{E}^2 + \frac{1}{\mu_0}\mathbf{B}^2\right)

← Older revision		Revision as of 22:22, 5 April 2017
Line 1:		Line 1:
−	Here is a list of important equations that have been empirically found to be tested in UCLA's comprehensive exams. Feel free to add further equations for good practice (often, an equation can be copied from the corresponding open source wikipedia article). You may also link to good articles on Wikipedia or upload your own questions and solutions ~~(Please do not submit copyrighted work without permission)~~.	+	Here is a list of important equations that have been empirically found to be tested in UCLA's comprehensive exams. Feel free to add further equations for good practice (often, an equation can be copied from the corresponding open source wikipedia article). You may also link to good articles on Wikipedia or upload your own questions and solutions.

	<div class="fb-share-button" data-href="http://developers.facebook.com/docs/plugins/" data-type="button_count"></div>		<div class="fb-share-button" data-href="http://developers.facebook.com/docs/plugins/" data-type="button_count"></div>

@@ Line 102: / Line 102: @@
 </div>
-  Wavefunctions of pauli matrix operators: <div class="mw-collapsible mw-collapsed" style="width:750px">
+  Eigenstates of pauli matrix operators: <div class="mw-collapsible mw-collapsed" style="width:750px">
   \[
 \begin{array}{lclc}
@@ Line 113: / Line 113: @@
   </div>
-Operate $\sigma_{i}$ on $|\pm\rangle$:<div class="mw-collapsible mw-collapsed" style="width:750px">
+Using Pauli matrices and $S_z$ eigenstates, operate $\sigma_{i}$ on $|\pm\rangle$:<div class="mw-collapsible mw-collapsed" style="width:750px">
   \[
 \sigma_{z}|\pm\rangle = \pm |\pm\rangle \\

@@ Line 76: / Line 76: @@
 '''Spin Systems'''
   Pauli Matrices: <div class="mw-collapsible mw-collapsed" style="width:750px">
-\[
+ \[
 \sigma_x= \begin{pmatrix}
 &1\\
@@ Line 113: / Line 113: @@
   </div>
-For $(S.n) |n; \pm \rangle = \pm \frac{\hbar}{2} |n; \pm \rangle $, express $| n; \pm \rangle$ in $|z; \pm\rangle$ basis:<div class="mw-collapsible mw-collapsed" style="width:750px">
+Operate $\sigma_{i}$ on $|\pm\rangle$:<div class="mw-collapsible mw-collapsed" style="width:750px">
-\[
+For $(S.n) |n; \pm \rangle = \pm \frac{\hbar}{2} |n; \pm \rangle $, express $| n; \pm \rangle$ in $|z; \pm\rangle$ basis:<div class="mw-collapsible mw-collapsed" style="width:750px">
 |n ; +\rangle = \cos(\frac{\theta}{2}) e^{-i\phi} |+\rangle + \sin(\frac{\theta}{2}) |-\rangle =\begin{pmatrix}
 \cos(\frac{\theta}{2}) e^{-i\phi} \\

@@ Line 824: / Line 824: @@
 </div>
-Compare [CM Course Notes].
+Compare [[CM Course Notes]].
 <br/>