http://sites.science.oregonstate.edu/portfolioswiki/ 2020-01-27T00:45:11-08:00 http://sites.science.oregonstate.edu/portfolioswiki/ http://sites.science.oregonstate.edu/portfolioswiki/lib/images/favicon.ico text/html 2013-07-29T11:27:02-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:cfswdiffeq?rev=1375122422 The Prompt Solve the differential equation, $$ \frac{d^{2}\psi}{d\phi^{2}}=\frac{-2m_{e}r_{o}^{2}E\psi}{\hbar^{2}} $$ Context This SWBQ Wrap Up [Powerpoint slide] [PDF slide] text/html 2013-07-29T11:28:20-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:cfswenergyfree?rev=1375122500 The Prompt What's the Energy of a Free Particle? Context This SWBQ Wrap Up [Powerpoint slide] [PDF slide] text/html 2013-07-29T11:29:41-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:cfswhamilfree?rev=1375122581 The Prompt What's the Hamiltonian of a Free Particle? Context This SWBQ Wrap Up [Powerpoint slide] [PDF slide] text/html 2013-07-29T11:38:34-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:cfswradialwave?rev=1375123114 The Prompt Given that $$ \rho=\frac{r}{a_{o}} $$ and $$ R(\rho)=\rho^{l}e^{-l\rho}H(\rho) $$ Find the radial wave function R(r) when n=3, l=2, m=2, and when n=3, l=1, and m=0. Context This SWBQ Wrap Up [Powerpoint slide] [PDF slide] text/html 2013-07-29T11:39:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:cfswring?rev=1375123188 The Prompt What questions can you ask about the particle on a ring system? Context This SWBQ Wrap Up [Powerpoint slide] [PDF slide] text/html 2013-07-29T11:42:02-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:cfswsphericalharm?rev=1375123322 The Prompt What would you expect to be the result of $H\vert l,m\rangle$? Context This SWBQ Wrap Up [Powerpoint slide] [PDF slide] text/html 2013-07-29T11:43:34-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:cfswtransition?rev=1375123414 The Prompt Looking at the spectral lines of hydrogen, use Rydberg's formula to investigate a particular line. Context This SWBQ Wrap Up [Powerpoint slide] [PDF slide] text/html 2012-08-23T22:24:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:index?rev=1345785846 text/html 2013-07-29T09:21:31-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:ppswbound?rev=1375114891 The Prompt “Graphically represent any bound state you can think of.” Context This SWBQ is useful for making connections between the energies observed in classical systems and those in quantum systems. Students will also have the opportunity to reflect on where they have previously encountered bound states in physics and how these bound states are commonly represented physically or graphically. text/html 2012-08-31T10:05:09-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:ppsweigenstateshow?rev=1346432709 Prompt “Show that $$\begin{bmatrix} 1 \\ 1 \end{bmatrix} \text{ and } \begin{bmatrix} 1 \\ -1 \end{bmatrix}$$ are eigenvectors of the 2-well system Hamiltonian, and find the eigenvalues. ” Context This SWBQ designs to be a small review for finding eigenvectors and eigenvalues, and also gives a glimpse into the general strategy for calculating the energies of eigenstates in the larger N-well system. text/html 2013-07-29T09:27:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:ppswidentify?rev=1375115226 The Prompt “Write down an example of a periodic system from any context.” Context This SWBQ Wrap Up Although very common in solid state physics, periodic systems can be found in a multitude of contexts in physics or otherwise. This activity challenges students to think about periodic systems in contexts they have previously encountered. By asking this question, the instructor can also gauge how familiar the class is with periodic systems and help clarify any inconsistencies in studen… text/html 2013-07-29T09:29:50-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:ppswlcao?rev=1375115390 The Prompt Consider a 3-chain potential well system with separation distance a. Recall the enevelope function for an electron in a potential landscape with N wells can be described with, $$ \psi(x)=\sum_{n=1}^{N}A\sin(kna)\phi(x-na) $$ text/html 2013-07-29T09:37:22-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:ppswsingleosc?rev=1375115842 The Prompt “A single particle is allowed to move between two fixed points. The springs both have spring constant $\kappa$. What is the differential equation that tells this atom what to do?” Context This SWBQ will help gauge how familiar students are with describing classical harmonic oscillators (particularly through use of Hooke's Law) in terms of differential equations. text/html 2017-03-15T09:51:52-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spangmomrev?rev=1489596712 Prompt Write down something you know about angular momentum. Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2015-08-11T13:37:09-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spsw3statecomprel?rev=1439325429 The Prompt “Write down the completeness relation for the general 3-state case.” Context After the completeness relation has been presented in the most familiar context of the spin-$\dfrac{1}{2}$ system, practice converting the same concept to a system with more states is useful for solidifying the general concept of the completeness relation. This small white board question also helps the instructor check who understands the general concept of the completeness relation and who still nee… text/html 2017-03-16T15:48:44-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswcompletenessrelation?rev=1489704524 Prompt Use the completeness relation to write $\vert + \rangle$ in the $\vert \pm \rangle_y$ basis. Context This SWBQ ... Based on a Colorado Clicker Question. Wrap Up [Powerpoint slide] [PDF slide] text/html 2015-08-13T13:11:51-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswcompoutprod?rev=1439496711 The Prompt “Compute the outer product $\vert +\rangle \langle +\vert$”. “Write down the projection operator for $\vert +\rangle_{x}$ in the z-basis in matrix and Bra-Ket notation. Then compute the outer product in the z-basis.” Context Oftentimes, students have been told that the outer product is a non-allowed matrix operation. Considering the outer product is essential for finding projection operators in quantum mechanical systems, these small white board questions are important f… text/html 2015-08-11T13:44:27-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswdensopprop?rev=1439325867 The Prompt Compute the outer product of the general state vector $$ \vert \psi\rangle=\left[\begin{array}{c} \sin(\frac{\theta}{2})\\ \cos(\frac{\theta}{2})e^{i\phi}\\ \end{array}\right] $$ Take the determinant of the computed 2 x 2 matrix. text/html 2017-03-16T15:48:32-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswdiracprojop?rev=1489704512 Prompt What happens when the outer product $\vert + \rangle\langle + \vert$ acts on $\vert\psi\rangle$? Context This SWBQ ... Based on a Colorado Clicker Question. Wrap Up [Powerpoint slide] [PDF slide] text/html 2016-08-02T15:49:25-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswdownupxcompute?rev=1470178165 The Prompt “Compute the inner product $_{x}\langle -\vert +\rangle_{x}$.” Context This SWBQ could be used in two different ways. For students that are in the process of finding defining $\vert+ \rangle_{x}$ and $\vert- \rangle_{x}$ in terms of the $z$-basis, this small white board question can be given to the students to help them find the relative phase between the $\vert -\rangle_z$ components of the two states. FIXME (See section ?.? in McIntyre). If students have already found wha… text/html 2017-02-23T11:45:36-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswdrawnormwf1?rev=1487879136 Prompt Draw the probability distribution of a normalized wave function. Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-02-23T11:49:33-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswdrawnormwf2?rev=1487879373 Prompt Draw the plot of a normalized wave function. Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-03-21T10:32:56-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spsweangmomrev?rev=1490117576 [Paul: I think this should become a sequence of SWBQ/Clicker to match what is in the binder.] Prompt Write down something you know about angular momentum. Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-03-16T15:49:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswinterpdfwfplot?rev=1489704540 Prompt How would you physically interpret the wave function in the sketch? Context This SWBQ ... Based on a Colorado Clicker Question. Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-02-23T11:39:56-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswinterpretwfplot?rev=1487878796 Prompt Physically interpret the wave function in the sketch. Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-02-23T11:34:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswintervalprobability?rev=1487878446 Prompt Prob(particle is between $x$ and $x + dx$) $= \vert\psi(x) \vert^2 dx$. What can you conclude? Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-03-16T15:48:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswkettomatrix?rev=1489704492 Prompt In a Spin-1 system, could $\vert 1 \rangle_x$ be represented with the matrix $\pmatrix{1\cr 0\cr 0\cr}$? Context This SWBQ ... Based on a Colorado Clicker Question. Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-03-16T15:48:25-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswkettomatrixnewbasis?rev=1489704505 Prompt Write the spin-half state $\vert + \rangle$ in the matrix representation of the $\vert \pm \rangle_y$ basis. Context This SWBQ ... Based on a Colorado Clicker Question. Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-03-16T15:49:18-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswlinmomentumunits?rev=1489704558 Prompt Which one of the following has the correct units for linear momentum ($\lambda=$ wavelength, $k=$ wavenumber$=2\pi/\lambda$, $m=$ mass? Context This SWBQ ... Based on a Colorado Clicker Question. Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-03-16T15:49:24-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswmomdifop?rev=1489704564 Prompt Starting with a “wave solution” $\psi(x,t)=A\exp[i(kx-wt)]$, how can one obtain a factor of k (perhaps with other factors)? Use the operator... Context This SWBQ ... Based on a Colorado Clicker Question. Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-02-23T14:15:18-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswmomentumexpectval?rev=1487888118 Prompt Write the integral form of the expectation value of momentum, $\langle\hat{p}\rangle=\langle\psi\vert\hat{p}\vert\psi\rangle$. Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-03-16T15:49:29-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswmomexpval?rev=1489704569 Prompt $\langle\hat{p}\rangle=\langle\psi\vert\hat{p}\vert\psi\rangle=$ ? Context This SWBQ ... Based on a Colorado Clicker Question. Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-03-16T15:49:05-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswnormprobdens?rev=1489704545 Prompt Is the wave function $\psi=\psi(x)$ shown normalized? Note that this is a plot of $\vert\psi\vert^2$ vs $x$. Context This SWBQ ... Based on a Colorado Clicker Question. Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-03-16T15:49:11-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswnormwf?rev=1489704551 Prompt Is this wave function normalized? (This wave function is pure real) Context This SWBQ ... Based on a Colorado Clicker Question. Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-03-16T15:48:37-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswoutprodmatrix?rev=1489704517 Prompt Write the outer product $\vert + \rangle\langle + \vert$ in matrix notation. Write the sum of outer products $\vert + \rangle\langle + \vert \ + \ \vert - \rangle\langle - \vert$ in matrix notation. Context This SWBQ ... text/html 2017-02-23T11:00:35-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswoutprodonwf?rev=1487876435 Prompt What happens when the outer product $\vert + \rangle\langle + \vert$ acts on $\vert\psi\rangle$? Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2015-08-11T13:49:49-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswoverallphase?rev=1439326189 The Prompt Given $$ \vert \psi(t)\rangle=c_{1}(0)e^{\frac{-iE_{1}t}{\hbar}}\vert E_{1}\rangle+c_{2}(0)e^{\frac{-iE_{2}t}{\hbar}}\vert E_{2}\rangle \, , $$ factor out an overall phase of $e^{\frac{-iE_{1}t}{\hbar}}$ from the quantum state. text/html 2017-03-16T17:24:29-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswpaulswbqsequence?rev=1489710269 Prompt Prompt 1 Prompt 2 Prompt 3 Prompt 4 Prompt 5 Prompt 6 Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2016-08-02T14:16:55-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswprobblanks?rev=1470172615 The Prompt ``How would you represent the probability of the following output using bra-ket notation?'' Context After using the SPINS Stern-Gerlach simulator for experimentation, students benefit from revisiting how the experimental setup is represented in bra-ket notation. This small whiteboard question is useful for exercising students' ability to move between different representations. Here, students must translate the physical experiment text/html 2013-07-29T11:10:17-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswpropblanks?rev=1375121417 The Prompt How would you represent the following output using bra-ket notation? (See figure in .pdf or .ppt.) [Powerpoint slide] [PDF slide] Context This SWBQ ... Wrap Up text/html 2017-02-23T12:08:38-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswspin1xbasisunitvector?rev=1487880518 Prompt Write the spin-1 system $\vert 1 \rangle_x$ in matrix notation. Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2015-08-11T12:51:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswspinguess?rev=1439322686 The Prompt “Write down what you think $\vert + \rangle_{x}$ is in the $z$-orientation basis.” Context This SWBQ has multiple purposes. We want students to be able to write a mathematical statement based on their experimental observations from SPINS Lab 1. However, they are not yet ready to do so precisely. Having this be open-ended and ill-defined pushes students to see if they can write a simple statement that makes sense based on their observations. Though this SWBQ is intended t… text/html 2017-02-23T10:57:27-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswspinhalfbasisconversion?rev=1487876247 Prompt Write the spin-half state $\vert + \rangle$ in the matrix representation of the $\vert \pm \rangle_y$ basis. Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2013-07-29T11:16:52-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswssquaredmatrix?rev=1375121812 The Prompt Using matrix notation, calculate $S^{2}$, when $$ S^{2}=S_{x}^{2}+S_{y}^{2}+S_{z}^{2} $$ Context This SWBQ is a great introduction to the S-squared operator and prepares students to think about this operator in the spin-1 system. Students are often surprised to see that after factoring out constant terms, $S_{x}^{2}$, $S_{y}^{2}$, and $S_{z}^{2}$ each become the identity matrix. The resulting constant term $\frac{3}{4}\hbar^{2}$ left over after adding the squared operators can… text/html 2015-08-11T13:24:31-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswstatecollapse?rev=1439324671 The Prompt Using the Stern-Gerlach Experiment, write down the state exiting the spin up port in bra-ket notation. (An x-oriented Stern-Gerlach device with an arbitrary quantum state $\vert \phi\rangle$ fired into it is drawn on the board.) text/html 2015-08-11T13:34:15-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswszoperator?rev=1439325255 Prompt “Write down what you think the $S_{z}$ operator is in matrix form.” Context This SWBQ offers students a chance to guess the $S_{z}$ operator and learn the process of how to find the $S$ operators in each orientation. Although students typically know that the $z$-oriented Stern-Gerlach experiment is directly related to the $S_{z}$ operator and that the result from a measurement is $\pm \frac{\hbar}{2}$, most may not know that these facts directly translate into matrix form. Of… text/html 2017-03-16T15:34:25-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswvelocityhamiltonian?rev=1489703665 Prompt Given that $\xhat\stackrel{.}{=}x$ and $\hat{p}_x\stackrel{.}{=}-i\hbar\frac{d}{dx}$, what is the hamiltonian operator? Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-03-16T15:48:56-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswwfdimensions?rev=1489704536 Prompt Given $\int_{-\infty}^{\infty} \vert\psi (x) \vert^2 dx = 1$, what are the dimensions of the wave function? Context This SWBQ ... Based on a Colorado Clicker Question. Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-02-23T11:59:41-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswwfmanip?rev=1487879981 Prompt Starting with a “wave solution” $\psi(x,t)=A\exp[i(kx-wt)]$, perform some mathematical operation that results in a factor of k. Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-03-16T15:48:50-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spswwfprobdensimp?rev=1489704530 Prompt Prob(particle is between $x$ and $x + dx$) $= \vert\psi(x) \vert^2 dx$. What conclusion can you draw? Context This SWBQ ... Based on a Colorado Clicker Question. Wrap Up [Powerpoint slide] [PDF slide] text/html 2017-03-15T09:50:38-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:spvelocityhamiltonian?rev=1489596638 Prompt Given that $\xhat\stackrel{.}{=}x$ and $\hat{p}_x\stackrel{.}{=}-i\hbar\frac{d}{dx}$, what is the hamiltonian operator? Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2015-08-06T18:50:30-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:title?rev=1438912230 Quantum Mechanics SWBQs text/html 2012-08-28T10:21:54-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:wvsweigvalq?rev=1346174514 Prompt “Write down an example of an eigenvalue equation.” Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2012-08-28T10:23:23-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:wvswexpectham?rev=1346174603 Prompt “Write the expectation value for the Hamiltonian operator for a system described by the state vector $\psi$.” Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2012-08-28T10:20:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:wvswinfinite?rev=1346174458 Prompt “Draw the first three wave functions for an infinite potential well.” Context This SWBQ ... Wrap Up [Powerpoint slide] [PDF slide] text/html 2013-07-24T11:16:11-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:wvswnorm?rev=1374689771 Prompt “Normalize one of the two following wave functions:” $$\psi(x) = \begin{cases} 0, & \text{if $x$ < 0} \\ sin(\frac{\pi{x}}{L}), & \text{if 0 < $x$ < $L$}\\ 0, & \text{if $x$ > $L$} \end{cases} $$ $$\psi(x) = \begin{cases} 0, & \text{if} \; x < -\frac{L}{2} \\ cos(\frac{\pi{x}}{L}), & \text{if} \; -\frac{L}{2} < x < \frac{L}{2}\\ 0, & \text{if} \; x > \frac{L}{2} \end{cases} $$ text/html 2012-08-27T10:00:56-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:wvswortho?rev=1346086856 Prompt ” Write down the orthogonality relationship” $$\boldsymbol{\langle\varphi_m \vert \varphi_n\rangle=\delta_{mn}}$$ “in wavefunction form.” Context This SWBQ is used to help the students to comfortably go between one representation of a quantum state to another. text/html 2013-07-26T11:54:05-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:wvswschrodinger?rev=1374864845 The Prompt Write down Schroedinger's Equation. FIXME: useful for some classes, but perhaps not a top priority Context This SWBQ Wrap Up [Powerpoint slide] [PDF slide] text/html 2013-07-26T11:56:19-08:00 http://sites.science.oregonstate.edu/portfolioswiki/swbq:qmsw:wvswsuperpose?rev=1374864979 The Prompt $$\vert\Phi\rangle=\frac{1}{\sqrt{5}}\vert\varphi_1\rangle+\sqrt{\frac{3}{5}}\vert\varphi_2\rangle+\frac{1}{\sqrt{5}}\vert\varphi_3\rangle$$ Is this superposition of energy eigenfunctions itself an eigenfunction of the Hamiltonian? Calculate the average value of $x$. Calculate $\langle H^2 \rangle$ What is the time dependence of the state vector?