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Math Help - Particle in a box (wavefunction problem)

  1. #1
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    Particle in a box (wavefunction problem)

    There is a particle in a box from -a to a (i.e. length of box = 2a) with the following wavefunction:

    ψ(x,0) = C(a−x) when |x| < a
    ψ(x,0) = 0 when |x| > a

    where C is a constant.

    Find a value of C such that ψ(x,0) is normalised and hence write down the corresponding probability density.

    To do this I tried ∫|ψ(x,0)| = 1 from -a to a

    = ∫ (ψ*(x,0) times ψ(x,0)) = C(a−x)(a−x) and followed on from here.
    Does this look right?
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  2. #2
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    Quote Originally Posted by Unoticed View Post
    There is a particle in a box from -a to a (i.e. length of box = 2a) with the following wavefunction:

    ψ(x,0) = C(a−x) when |x| < a
    ψ(x,0) = 0 when |x| > a

    where C is a constant.

    Find a value of C such that ψ(x,0) is normalised and hence write down the corresponding probability density.

    To do this I tried ∫|ψ(x,0)| = 1 from -a to a

    = ∫ (ψ*(x,0) times ψ(x,0)) = C(a−x)(a−x) and followed on from here.
    Does this look right?
    Yes.
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  3. #3
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    Thanks, just to make sure; is the probability density in this case just:
    C(a−x)(a−x) ?
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  4. #4
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    Quote Originally Posted by Unoticed View Post
    Thanks, just to make sure; is the probability density in this case just:
    C(a−x)(a−x) ?
    Yes. Note that in this case it is a "linear probability density" not a "volume probability density," though you probably already knew that.

    -Dan
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