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Particle in a box

  1. Dec 2, 2004 #1

    Can someone please explain to me how I should go about solving the following 2 questions?

    #1 The lowest energy level in a particle confined to a one-dimensional region of space with fixed dimension "L" is Eo. If an identical particle is confined to a similar region with the fixed distance (1/4)L, what is the energy of the lowest energy level that the particles have in common? Express in terms of Eo.

    #2 Consider a particle in a box of width "L" and let the particle be in a state n = 11. What is the first value of x, larger then 0, where the probability of finding the particle is the highest?
     
  2. jcsd
  3. Dec 2, 2004 #2

    Galileo

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    If these are questions concerning the infinite square well, use the fact that the energy levels are:
    [tex]E_n=n^2
    \frac{\pi^2\hbar^2}{2mL^2}[/tex]
    for n=1,2,3,...
     
  4. Dec 2, 2004 #3

    jtbell

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    Write down the probability distribution for the general case with arbitrary n. (You may need to start with the wave function and find the probabilty distribution from that.) Substitute n = 11. For the particle in a box, it should be pretty obvious where the maxima are, from the general form of the probability distribution. Sketching a graph of it might help.
     
  5. Dec 2, 2004 #4

    Dr Transport

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    FOr the first part of the problem

    [tex] E_{0} = \frac{\pi^2\hbar^2}{2mL^2} [/tex]

    for the smaller width box

    [tex] E_{n} = 4n^{2}\frac{\pi^2\hbar^2}{2mL^2} = 4n^2 E_{0} [/tex]

    from here figure it out.
     
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