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    Splitting a single light source into two out-of-phase sources?

    I've been contemplating an experiment on a 1-dimensional system which would require a single light source to be split into two separate sources which are exactly out of phase with each other. The idea is to focus the beams near each other (but not overlapping) along the 1D object. Any phonons...
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    HPLC Question

    Thanks weezilla - that helps a lot. I'm not actually using an autosampler - I have a custom application that will require multiple punctures (maybe several dozen) without changing vials (it's a long story). These vials are the perfect size, so I was just wondering about the caps. Thanks again.
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    HPLC Question

    I have a question about https://www.amazon.com/dp/B002RS5IKA/?tag=pfamazon01-20 product. It is an autosampler shell vial with a polyethylene plug style needle closure. Does anyone know whether the plug on this vial will be resealable? In other words, will it be able to withstand multiple...
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    Optics question - laser power sources

    We have a 532 nm laser that we use with our Raman tool. The only power indicator on the control is in the form of a percentage. I know that at 100%, the laser has a power of 25 mW. Does this scale linearly with power percentage? In other words, does 50% power translate to 12.5 mW?
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    Integral Notation Question

    I saw this notation in a textbook but I'm a bit confused by it. What exactly does the 3 mean? Is it shorthand for a triple integral in spherical coordinates? \int{d^3 r} Thanks in advance.
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    A wiki for equations

    A colleague of mine just started a website called wikiquation.com. It's a searchable wiki-style database for equations. The database is currently quite empty, so it's not very useful as a search engine yet, but it allows anyone to add or edit an equation without creating a user account. I think...
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    Physics History

    Yes, that link is perfect! I never tried googling the exact quote because I assumed my version of the quote was off, but I underestimated my own memory. It was definitely Compton. Here is a quote from the source cited above:
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    Physics History

    One of my professors told me a story about a physicist and I can't remember who it was. It's driving me crazy. This is what I remember about the story. Apparently this physicist was a new faculty member and he had a seemingly brilliant plan for some experiment. All of the older faculty members...
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    Any good books on how to do research?

    I'm looking for a book that gives advice on how to research as a professional scientist. I am looking for insight into the culture of industrial research, applying for grants and obtaining funding, methods and techniques to use time your time effectively, etc. I'd prefer something from a physics...
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    On/Off Ratio

    Research-related question: What is the typical on/off ratio of a silicon transistor? This seems like basic information, but I can't find it anywhere. Also, how high does the on/off ration need to be in order for transistors (say, in a logic circuit) to function correctly? Thanks!
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    Research: Applied vs. Fundamental

    I'm graduating with a B.S. in physics and I will soon be starting a Ph.D. program in nanoscale science, which is essentially an applied physics program. I chose this program because my undergraduate research was focused in this area and I've really enjoyed it. However, I'm wondering if my...
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    Help with Eigenvalues problem

    Homework Statement True/False If Ttheta is a rotation of the Euclidean plane R2 counterclockwise through an angle theta, then T can be represented by an orthogonal matrix P whose eigenvalues are lambda1 = 1 and lambda2 = -1. Homework Equations The Attempt at a Solution Just checking to...
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    Finding eigenvalues of matrix

    Aha. That makes sense now.
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    Finding eigenvalues of matrix

    Very good point. Thanks!
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    Finding eigenvalues of matrix

    I was just doing two steps at once. Bad form on my part.
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    Finding eigenvalues of matrix

    Oh, duh. Since there are two terms on the RHS and they are constants then the must both be equal to zero separately. Haha.
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    Finding eigenvalues of matrix

    Because it was much easier to do that than it was to multiply everything out and try to factor a third-degree polynomial.
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    Finding eigenvalues of matrix

    Thanks for your help. So let me get this straight. Whenever I divide by a term to cancel it, I count that term as one of my solutions, right? Does this always work? I didn't quite understand what you meant by testing two separate cases.
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    Finding eigenvalues of matrix

    Homework Statement Find the eigenvalues of the following matrix: \left( \begin{array}{ccc} 1 & 0 & -3 \\ 1 & 2 & 1 \\ -3 & 0 & 1 \end{array} \right) Homework Equations The Attempt at a Solution I think I'm forgetting a basic algebra rule or something. I know there are supposed to be...
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    Linear Algebra (Similar Matrices)

    Ah yes, I see. I was thinking of T as a vector instead of a transformation. Thanks!
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    Linear Algebra (Similar Matrices)

    Homework Statement Write the standard matrix representation TE for T. Homework Equations T\left(ax^3+bx^2+cx+d\right)=(a-b)x^2+(c-d)x+(a+b-c) The Attempt at a Solution [T]_E=\left( \begin{array}{c} a+b-c \\ c-d \\ a-b \\ 0 \end{array} \right) I think this is right, but a...
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    Linear Algebra (Change of Basis)

    I see. so a valid test would be: \left( \begin{array}{cccc} 1 & 1 & 1 & 1 \\ 1 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{array} \right).\left( \begin{array}{c} 0 \\ 0 \\ 1 \\ 0 \end{array} \right)=\left( \begin{array}{c} 1 \\ 0 \\ -1 \\ 0 \end{array} \right) And the...
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    Linear Algebra (Change of Basis)

    Homework Statement Let E={1, x, x2,x3} be the standard ordered basis for the space P3. Show that G={1+x,1-x,1-x2,1-x3} is also a basis for P3, and write the change of basis matrix S from G to E. Homework Equations The Attempt at a Solution Here's what I got: S_E^G=\left(...
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    Another Linear Transformation

    Thanks! There are two 1's in the third column of the first matrix because there is an x3 in the first and last element of T1 (is that the right terminology?)
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    Another Linear Transformation

    Is this right, then? A=\left( \begin{array}{ccc} 0 & 0 & 1 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{array} \right)\cdot \left( \begin{array}{ccc} -1 & 0 & 1 \\ -1 & -2 & 1 \\ 1 & 0 & -1 \end{array} \right)=\left( \begin{array}{ccc} 1 & 0 & -1 \\ 1 & 0 & -1 \\ 1 & 0 & -1 \end{array} \right)
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    Another Linear Transformation

    Homework Statement This is a slight variation of the last problem I posted. Write the standard matrix representation for T1T2 and use it to find [T1T2(1,-3,0)]E. Homework Equations T_1\left(x_1,x_2,x_3\right)=\left(x_3,-x_1,x_3\right)...
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    Linear Transformation

    Yes, these things often depend on the textbook. Thanks.
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    Linear Transformation

    Thank you both for your input!
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    Linear Transformation

    Homework Statement Write the standard matrix representation for T1 and use it to find [T1(1,-3,0)]E. Homework Equations T_1\left(x_1,x_2,x_3\right)=\left(x_3,-x_1,x_3\right) The Attempt at a Solution I just wanted to check to see if I am doing this right. Thanks in advance! A=\left(...
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    Linear Algebra (Span)

    Oh, I see. So the fact that they are 3 linearly independent vectors means that they do span R^3. Got it. Thanks!
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