Recent content by aimforclarity

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    Autocorrelation of a wiener process

    ok, so can I say <e^{\phi(t)+\phi(t+\tau)}>=<e^{\phi(t)+\phi(t)+\phi(\tau)}> since W(t+\Delta t)=W(t)+W(\Delta t). Next we can say <e^{\phi(t)+\phi(t)+\phi(\tau)}>=<e^{2\phi(t)}><e^{\phi(\tau)}> because <\phi(t)\phi(\tau)>=0
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    Autocorrelation of a wiener process

    Let \phi(t) be a Brownian Walk (Wiener Process), where \phi\in[0,2\pi). As such we work with the variable z(t)=e^{i\phi(t)}. I would like to calculate E(z(t)z(t+\tau)) This is equal to E(e^{i\phi(t)+i\phi(t+\tau)}) and I know that E(e^{i\phi(t)})=e^{-\frac{1}{2}\sigma^{2}(t)}, where the...
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    Brownian motion solves Laplace's Equation?

    There seems to be a curious connection between Brownian Motion, stochastic diffusion process, and EM. http://en.wikipedia.org/wiki/Stochastic_processes_and_boundary_value_problems I was hoping to share and to have someone add some insight on on what it means that the Dirichlet boundary...
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    LaTeX Custom Mathematica Shortcut: Copy as LateX

    This can be very useful, so I thought i'd share. If you edit the > Wolfram Research\Mathematica\8.0\SystemFiles\FrontEnd\TextResources\Windows\MenuSetup.tr file you can make Strl+Shift+C copy not plain but in LateX format. Very useful. Look for the line in the file that says "&LaTeX"...
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    Quantum Numbers of Spin 1/2

    this sounds like a question that should be answered somewhere, but i cant find it. how many quantum numbers does it take to specify the state of a spin 1/2? 1. if it points along z, then just 1: the eigenvalue of Sz will do (up to global phase) A. whether or not in a B field B. if...
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    What is Information?

    im not sure thats any better. just because 200 years ago we could not "point to" or manipulate say cooper pairs or atoms, doesn't mean they dont exist and don't have an effect. this is a real problem in physics, how do we see and manipualte, people are discovering new ways every so often...
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    Complex Conjugate: just replace i by -i even in denominator or inside argument?

    so i think it works for any function with a taylor expansion (~analytic), because conjugation carries through addition and multiplication and so through powers and thus exponents 1. (z1 +z2)* = z1*+z2* 2. (z1 z2)* = z1* z2* 3. (z1^n)* = z1*^n 4. \left(\frac{1}{\text{z1}}\right)^* =...
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    SHO Ladder Method missed states?

    Thanks a lot!
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    What is Information?

    yes, you are saying that information is a human construct and does not exit beyond us, like the alphabet or the idea of the color green. this is true, the concept of information is 'artifical' in the sense that as a concept it is not ontological (does not exist), but like all human concepts...
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    Complex Conjugate: just replace i by -i even in denominator or inside argument?

    this is very good, that is what i was asking! Thank you, so it works almost all the time. do you know when, in what cases i should be careful when using it? ie anytime i dont use fractions and logs, and exponetnials and trig funcs?
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    Complex Conjugate: just replace i by -i even in denominator or inside argument?

    see my post right above yours, i know that the complex conjugate is only equal to the complex # itself when the number is real, i am asking how to get the complex conjugate
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    What is Information?

    i agree, i think this is the essence of heisengber uncertainty and infromation. for something to be ontological (that it can exist), it must have effect, and must be also epistomological (knowable), we must be able to know about it, to learn it is there. we can only deal with things we...
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    SHO Ladder Method missed states?

    this is all true, and is a summary of grifits derivation, but it it doesn't tell you that the raising and lowering operators take you between nearest orthogonal states. what is they raised and lowered by two quanta of energy, how do you know what the smallest quanta of energy is?
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    Complex Conjugate: just replace i by -i even in denominator or inside argument?

    this is basically the answer to my question, but i do need to unravel its meaning: 1. holomorphic - basically well behaved, has derivatives. 2. phi(z) is real for z in reals, this is a hard condition, because often the form of the expression is not such, but i have found that the trick...
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    Complex Conjugate: just replace i by -i even in denominator or inside argument?

    to get a Complex Conjugate of a #, is it ok to just replace i by -i even in denominator or inside argument?
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