http://sites.science.oregonstate.edu/portfolioswiki/ 2020-01-27T00:57:09-08:00 http://sites.science.oregonstate.edu/portfolioswiki/ http://sites.science.oregonstate.edu/portfolioswiki/lib/images/favicon.ico text/html 2011-08-16T17:46:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecangularmomentum?rev=1313542002 Introduction to Angular Momentum Lecture ( minutes) [Central Forces Notes] Section 6 text/html 2011-08-16T17:46:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecassoclegpoly?rev=1313542002 Associated Legendre Polynomials Lecture (20 minutes) [Central Forces Notes] Section 25 text/html 2013-04-11T17:02:52-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cfleccenterofmass?rev=1365724972 Derivation and Explanation of Center of Mass Lecture (15 minutes) [Central Forces Notes] Section 3 --Survivor Outerspace Activity. text/html 2013-04-05T11:31:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cfleccentralforce?rev=1365186688 Definition of a Central Force Lecture [Central Forces Notes] Section 5 central text/html 2013-04-05T11:23:47-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cfleccfmotionassumptions?rev=1365186227 Interactive Lecture on Assumptions about Central Force Motion ( minutes) [Central Forces Notes] Section 5 $$m_1\dfrac{d^2}{dt^2}\vec{r}_1=\vec{F}_{1,ext}-\vec{f}_{12}$$ $$m_2\dfrac{d^2}{dt^2}\vec{r}_2=\vec{F}_{2,ext}+\vec{f}_{12}$$ text/html 2011-08-16T17:49:51-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecclassicallim?rev=1313542191 The Classical Limit Lecture ( minutes) [Hydrogen orbitals for large and small values of m] text/html 2011-08-16T17:46:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cfleceffpotential?rev=1313542002 Energy and Effective Potential Lecture (25 minutes) [Central Forces Notes] Sections 11 and 12 small whiteboard question text/html 2011-07-04T15:42:01-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflechydrogencalculations?rev=1309819321 Quantum Calculations on the Hydrogen Atom Lecture (60 minutes) $$P(-3 \hbar) = \sum^{\infty}_{n=4} \sum^{n-1}_{l=3} |\langle n, l, m| \Psi \rangle |^2$$ text/html 2011-08-16T17:46:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflechydrogenradialeq?rev=1313542002 Solving the Radial Equation Lecture (45 minutes) [Central Forces Notes] Section 28-30 text/html 2011-08-16T17:46:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflechydrogensols?rev=1313542002 Lecture ( minutes) [Central Forces Notes] Section 31 $${R_n}^\ell (r){Y_\ell }^m\left( \theta ,\phi \right) = \sqrt { { {\left( {\frac{2}{{n{a_0} } } } \right)}^3}\frac{{\left( {n - \ell - 1} \right)!} }{{2n{ {\left( {\left( {n + \ell } \right)!} \right)}^3} } } } {\left( {\frac{{2r} }{{n{a_0} } } } \right)^\ell }{e^{ - \frac{r}{ {n{a_0} } } } }L_{n + \ell }^{2\ell + 1}\left( {\frac{ {2r} }{ {n{a_0} } } } \right){Y_\ell }^m\left( {\theta ,\phi } \right)$$ text/html 2018-03-16T11:02:08-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cfleclegprops?rev=1521223328 Lecture (10 minutes) text/html 2011-08-16T17:46:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cfleclegseries?rev=1313542002 Legendre Series Lecture (20 minutes) [Central Forces Notes] Section 24 $$a_k = (k + \frac{1}{2})\int_{-1}^1 P_k(z)^* f(z) dz $$ Small Whiteboard Questions Students often struggle with this, but it is helpful to remind them of the way you find coefficients for a vector (by taking the dot product,, and coefficients for a Fourier series (the inner product for functions, Common Student Questions “” text/html 2012-03-14T14:18:40-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecloperators?rev=1331759920 Spherical Harmonics and the $H$, $L^2$, and $L_z$ Operators Lecture (60 minutes) [Central Forces Notes] Section 27 text/html 2013-04-11T16:59:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecorbitshape?rev=1365724766 Finding the Shape of the Orbit (Kepler's 1st Law) Lecture (25 minutes) [Central Forces Notes] Section 10 text/html 2016-07-11T13:45:05-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecpolar?rev=1468269905 Kepler's 2nd Law in Polar Coordinates Lecture (5 minutes) [Central Forces Notes] Section 8 Velocity and Acceleration in Polar Coordinates \begin{align*} \vec{L}&=\vec{r}\times\vec{p}\\ &=\vec{r}\times\mu\vec{v}\\ &=r\hat{r}\times\mu\left(\dot{r}\hat{r}+r\dot{\phi}\hat{\phi}\right)\\ &=\mu r^2\dot{\phi}\;\hat{r}\times\hat{\phi}\\ &=\mu r^2\dot{\phi}\hat{z}\text{ (cylindrical)}\\ &=-\mu r^2\dot{\phi}\hat{\theta}\text{ (spherical)} \end{align*} text/html 2013-04-11T16:56:07-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecpositionvec?rev=1365724567 Position Vector Lecture/Discussion (15 minutes) [Central Forces Notes] Section 7 text/html 2011-07-04T15:41:01-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecpostulatesofqm?rev=1309819261 Postulates of Quantum Mechanics Note: A common misconception among students first learning quantum mechanics is that a measurement is carried out by operating on a ket with the operator associated with observable one wants to measure. text/html 2011-08-16T17:46:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecradialeq?rev=1313542002 Finding the Radial Equation from Conservation of Energy Lecture (15 minutes) [Central Forces Notes] Section 11 text/html 2011-08-16T17:46:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecreducedmass?rev=1313542002 Derivation of Reduced Mass Lecture [Central Forces Notes] Section 4 $${{m_1 m_2}\over {m_1+m_2}} {d{^2}\over{d{t^2}}} (\Vec{r_1}-\Vec{r_2}) = \Vec{f_{12}}$$ text/html 2011-08-16T17:46:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecreducedmasshamiltonian?rev=1313542002 Lecture on the Derivation of the Hamiltonian in terms of Reduced Mass (20 minutes) [Central Forces Notes] Section 14. text/html 2011-08-16T17:46:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecreviewhamiltonian?rev=1313542002 Review of Hamiltonians Lecture (20 minutes) [Central Forces Notes] Section 13 This lecture reviews what students have learned about Schrödinger's equation and the Hamiltonian from previous classes. small whiteboard question $$\hat{H}= \frac{\hbar^2}{2 m_p} \nabla^2_p + \frac{\hbar^2}{2 m_e} \nabla^2_e -\frac{1}{4 \pi \epsilon_0} \frac{e^2}{|r_p-r_e|}$$ where $$\nabla^2_p = \frac{1}{r_p^2} \frac{\partial}{\partial r_p} \left(r_p^2 \frac{\partial}{\partial r_p} \right)+ \frac{1}{r_p^2 \sin(\t… text/html 2011-08-16T17:46:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecringangmomentum?rev=1313542002 Angular Momentum on the Ring Lecture (20 minutes) [Central Forces Notes] Section 18 text/html 2011-08-16T17:46:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecringeigenstates?rev=1313542002 Finding the Eigenstates for the Ring Lecture (30 minutes) [Central Forces Notes] Section 17 small whiteboard question text/html 2011-08-16T17:46:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecsepofvariables?rev=1313542002 Separation of Variables in Spherical Coordinates Lecture (30 minutes) [Central Forces Notes] Section 33 (Appendix B) and 16 text/html 2012-08-09T15:48:24-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecseriessoltheta?rev=1344552504 Solving the $\Theta$ Equation using the Series Solution Method (90 minutes) FIXME See 2012 video for series solution lecture with sequence of SWBQs. [Central Forces Notes] Section 20-23 Small White Board Questions Students sometimes have difficulty with this the first time they do it because they are not used to using the recurrence relation in this way. In addition, they do not realize that they need to set the values of $a_0$ and $a_1$. Common Student Confusions/Questions text/html 2013-04-11T15:39:52-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecsolveeqofmotion?rev=1365719992 Solution to the Central Force Equation of Motion in Polar Coordinates Lecture (30 minutes) [Central Forces Notes] Section 9 $$\mathbf{\hat{r}}:\; f(r)=\mu(\ddot{r}-r\dot{\phi}^2)$$ $$\mathbf{\hat{\phi}}:\;0=\mu(r\ddot{\phi}+2\dot{r}\dot{\phi})$$ text/html 2013-05-14T13:34:08-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecsphereharmonics?rev=1368563648 Spherical Harmonics, the Solutions to the Rigid Rotor Lecture (30 minutes) [Central Forces Notes] Section 26 One analogy that seems to resonate with students, especially the musicians is that spherical harmonics are essentially the harmonics for a spherical drum. text/html 2011-08-16T17:45:29-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cflecylmcombo?rev=1313541929 Combinations of $Y_{l,m}(\theta,\phi)$ and the Spherical Harmonic Series ( minutes) [Central Forces Notes] Section 26 text/html 2018-03-16T10:55:10-08:00 http://sites.science.oregonstate.edu/portfolioswiki/courses:lecture:cflec:cfmblec2d?rev=1521222910 Lecture (25 minutes) --