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Quantum Mechanics Particle moving in 1-D potential

  1. Mar 15, 2012 #1
    1. The problem statement, all variables and given/known data
    I've been attempting this one for a while now and so far it has been to no avail. The question itself is in the attached document.

    I am given an expression that defines the wavefunction moving in 1-D over an interval and the time component is fixed with t=0.

    2. Relevant equations

    〖|ψ(x,0)|〗^2 = prob dist, in which likelihood of finding a particle at that point can be inferred.


    3. The attempt at a solution

    first of all I assume that (A) is a complex constant and as a result i multiply the wavefunction by its conjugate to get the following,

    〖|ψ(x,0)|〗^2=|A|^2 (x^4-2x^3 a+x^2 a^2) which im not sure is correct and furthermore have no idea how to sketch it.

    any guidance would be appreciated!
     

    Attached Files:

  2. jcsd
  3. Mar 15, 2012 #2

    vela

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    That's correct, but it would probably be better not to multiply it out initially. Just leave it as
    $$|\Psi(x,0)|^2 =
    \begin{cases}
    |A|^2 (x-a)^2 x^2 & 0 \le x \le a \\
    0 & \text{otherwise}
    \end{cases}$$ Surely, you must have done curve sketching in algebra and calculus. Where does the function vanish? Where is it positive? Where is it negative? Where does it attain a maximum or a minimum?
     
  4. Mar 15, 2012 #3
    ahh yes that makes it alot clearer, thanks for the help!
     
  5. Mar 16, 2012 #4
    I'm also having difficulty with part b of this question.

    I tried using a symmetry approach to try and deduce the value of |A| but in my working the |A|^2 term ends up being cancelled which is of no use to me.

    again any pointers would be much appreciated.
     
  6. Mar 16, 2012 #5

    vela

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    You need to use the normalization condition to determine |A|.
     
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