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Thread: how to find the coefficient of wavefunctin of infty square well

  1. #1
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    how to find the coefficient of wavefunctin of infty square well

    if we know $\displaystyle \psi(x,0)=cx(a-x) $

    how to find c
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  2. #2
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    I guess the well has borders at 0 and a. Hence we know (with 100% probability) that particle is inside the well. Thus probability that particle is inside the well is 1:
    $\displaystyle \int_{0}^{a} \bigl|\psi(x)\bigr|^2dx = 1$

    We get
    $\displaystyle c^2 \int_{0}^{a} x^2(a - x)^2 dx = 1$
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  3. #3
    Senior Member bkarpuz's Avatar
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    Quote Originally Posted by silversand View Post
    if we know $\displaystyle \psi(x,0)=cx(a-x) $

    how to find c
    There must be some more information.
    There may be several ways to determinate $\displaystyle c$ with respect to the initial conditions.
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  4. #4
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    Quote Originally Posted by bkarpuz View Post
    There must be some more information.
    There may be several ways to determinate $\displaystyle c$ with respect to the initial conditions.
    I disagree. I've showed the way to calculate c, frankly speaking what we have here is an initial condition. We can calculate $\displaystyle \psi(x, t)$ expressing $\displaystyle \psi(x, 0)$ as linear combination of eigenfunctions.
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