Recent content by Gumbercules

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    How Do You Construct the Dual Basis in Dirac Notation?

    This makes sense. Thank you!
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    How Do You Construct the Dual Basis in Dirac Notation?

    Homework Statement my apologies if this question should be posted in the math forum 3-d space spanned by orthonormal basis: (kets) |1>, |2>, |3>. Ket |a> = i|1> - 2|2> - i|3>. Ket |b> = i|1> + 2|3>. The question is to construct <a| and <b| in terms of the dual basis (kets 1,2,3)...
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    Hilbert Space: f(x) = x^n on Interval (0,1)

    Thanks!
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    Hilbert Space: f(x) = x^n on Interval (0,1)

    Homework Statement for what range of n is the function f(x) = x^n in Hilbert space, on the interval (0,1)? assume n is real. Homework Equations functions in Hilbert space are square integrable from -inf to inf The Attempt at a Solution I am having trouble with the language of the...
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    QM: psi(x,t) for Gaussian Wave Packet

    Perhaps you are right Turin, I do feel a little braindead at the moment. Do you mean exp(a+b) = exp(a)exp(b)? In that case, I would take the exp((b^2)/4a) out of the integral, which would leave the integral from -inf to + inf (exp(-y^2)), which I can solve. My apologies if I have this wrong...
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    QM: psi(x,t) for Gaussian Wave Packet

    Homework Statement For a free particle, Given psi(x,0) = Aexp(-ax^2), find psi(x,t) Homework Equations phi(k) = 1/(sqrt(2pi)) times integral from -inf to +inf (psi(x,0)exp(-ikx))dx psi(x,t) = 1/(sqrt(2pi)) times integral from -inf to +inf (phi(k)exp(i(kx - (hk^2)t/2m)))dk my apologies...
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    How to Normalize the Wave Function ψ(x,t) = Ae^(-bx)e^(-iwt)?

    I've got it now, thank you very much, Turin!
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    How to Normalize the Wave Function ψ(x,t) = Ae^(-bx)e^(-iwt)?

    My apologies, I am somewhat fuzzy on my notions of transforms (I did Laplace and Fourier transforms, but that was several years ago with no practice since). I am thinking that I need a negative sign in the exponent to undo what the absolute value does, but I don't see how that will help without...
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    How to Normalize the Wave Function ψ(x,t) = Ae^(-bx)e^(-iwt)?

    sorry, yes, I'm not quite sure how to insert the math symbols. I checked the problem in the text again and I think the integral I looked up in the table is wrong as I neglected the absolute value. On top of that, the limits of integration were wrong as well. (must've been in a hurry, I guess)...
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    How to Normalize the Wave Function ψ(x,t) = Ae^(-bx)e^(-iwt)?

    Yep, that's what I was forgetting. Thank you!
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    How to Normalize the Wave Function ψ(x,t) = Ae^(-bx)e^(-iwt)?

    Homework Statement I am unfamiliar with LaTeX (is there a tutorial around, or should I just wing it and risk posting a potential mess?). my problem is that I need to normalize a wave function: psi(x,t) = Ae^(-bx)e^(-iwt). there are no constraints given. Homework Equations integral of...