Quantum physics

How can I solve the following ecercise: Use perturbation theory to calculate the energy levels of a particle in a box with a cosine function botto. Let the box extend from x=a to x=a and let the perturbing potential be H' = V0[1+cos(2*Pi*m*x/a)]. This potential oscilates between 2V0 y . The number of oscilations is determined by m. Discuss restrictions on the possible values of k+1 and k-1 in the integrals H'kl

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  1. What is a botto?

    Your sentence:
    << This potential oscilates between 2V0 y .>>
    appears to be incomplete.

    I don't think any of us are going to be able to answer this question.

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  2. bottom

    2V0 or 2V is the potential in x=0

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  3. How can I solve the following ecercise: Use perturbation theory to calculate the energy levels of a particle in a box with a cosine function bottom. Let the box extend from x=a to x=a and let the perturbing potential be H' = V0[1+cos(2*Pi*m*x/a)]. This potential oscilates between 2V0 y 0. The number of oscilations is determined by m. Discuss restrictions on the possible values of k+1 and k-1 in the integrals H'kl

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  4. I would shift x so that the box is from x = 0 to x = 2 a. The unperturbed states are then:

    psi_n(x) = a^(-1/2) sin[n pi x/)(2 a)]

    The perturbation is:

    H' = V0[1+cos(2*Pi*m*(x-a)/a)] =

    V0[1+cos(2*Pi*m*x/a)]

    The first order correction is:

    E1 = <psi_n|H'|psi_m> =

    Integral from x = 0 to 2 a of

    |psi_n|^2 H'(x) dx =

    1/a Integral from x = 0 to 2 a of sin^2[n pi x/)(2 a)]*
    V0[1+cos(2*Pi*m*x/a)] dx

    which is straightforward to evaluate.

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  5. Thanks Count Iblis, for understanding and answering this question. I should not have assumed none of us could answer it.

    I still don't understand the << This potential oscilates between 2V0 y 0. >>
    statement. Does the "y" represent Spanish "and" ?

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  6. Yes, it looks like "y" = "and". I think Juan also needs to consider the second order correction, because the question mentions the matrix elements H'kl, which occur in the second order corrections.

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  7. H'(x=0) = 2V0
    H'(X = a/2) = 0
    H'(x= a) = 2 V
    (y is and) in spanish
    and I don't know wath does mean k+1 and k-1. It refers to l=1?

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