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Quantum mechanics

  1. Jan 2, 2010 #1
    1. The problem statement, all variables and given/known data

    A particle is in a quantum state defined by:

    [tex]\Phi[/tex](x)=0.917[tex]\Psi_1[/tex]+0.316[tex]\Psi_2[/tex]+0.224[tex]\Psi_3[/tex]+a[tex]\Psi_4[/tex]

    where [tex]\Psi[/tex] are the eigenfunctions for a particle in a box given by [tex]\Psi_n[/tex]=[tex]\sqrt{2/L}[/tex]sin(npix/L).

    The corresponding eigenenergies are [tex]E_n[/tex]=1.5n^2eV

    What is the probability that an energy measurement will find the particle in its first excited state?

    2. Relevant equations

    i was thinking to use the integral of the initial state, multiplied by the eigenstate with the energy corresponding to the first excited state, but i am not really sure, it is more of a guess, so if someone could explain the logic to me it would ve appreciated. i always get stuck on the probability questions when they refer to the probability of specific energy states or momentum states> so i would like to understand this concept instead of just copying a method.



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 3, 2010 #2

    dextercioby

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    Homework Helper

    There's an axiom (some people call it the <Born rule>) telling you exactly what you need to find out: the probability of getting E_1 when measuring the energy. Search for it in your lecture notes.
     
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