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Quantum Oscillator

  1. Jun 4, 2010 #1
    1. The problem statement, all variables and given/known data
    Problem 8.
    1. Express the distance [tex]x_c[/tex] as a function of the mass [tex]m[/tex] and the restoring
    parameter [tex]c[/tex] used in Problem 7.

    (Problem 7.
    1. Calculate the energy of a particle subject to the potential [tex]V(x) = V_0 +
    cx^2/2[/tex] if the particle is in the third excited state.
    2. Calculate the energy eigenvalues for a particle moving in the potential
    [tex]V(x) = cx^2/2 + bx[/tex].)

    Quantum Mechanic. Chapter 3. Daniel B. Res.


    2. Relevant equations

    [tex]H=\frac{p^2}{2m}+\frac{m\omega ^2}{2}x^2[/tex]


    3. The attempt at a solution
    I cannot understand what is actually meant by this parameter [tex]x_c[/tex] and how to approach the problem.
     
  2. jcsd
  3. Jun 4, 2010 #2

    vela

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    It might help if you provided the complete problem statement for problem 8. The reference to problem 7 just means c is a spring constant; it doesn't say anything about what xc is supposed to represent.
     
  4. Jun 5, 2010 #3
    Problem 8.
    1. Express the distance [tex]x_c[/tex] as a function of the mass [tex]m[/tex] and the restoring
    parameter [tex]c[/tex] used in Problem 7.
    2. If [tex]c[/tex] is multiplied by 9, what is the separation between consecutive eigenvalues?
    3. Show that [tex]x_c[/tex] is the maximum displacement of a classical particle moving
    in a harmonic oscillator potential with an energy of [tex]\hbar\omega/2[/tex].
     
  5. Jun 5, 2010 #4

    vela

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    Well, your confusion is understandable if this is all the info you have. I have no idea how xc is defined either.
     
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