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Energy Spectrum for Hamiltonian

  1. Dec 11, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the energy spectrum of a system whose Hamiltonian is
    H=Ho+H'=[-(planks const)^2/2m][d^2/dx^2]+.5m(omega)^2x^2+ax^3+bx^4

    I gues my big question to begin is what exactly makes up the energy spectrum. I know the equation to the first and second order perturbations but Im not sure exactly what the energy spectrum entails. Please help.

    2. Relevant equations

    3. The attempt at a solution
    ive figured out that H'=ax^3+bx^4

    and Ho==[-(planks const)^2/2m][d^2/dx^2]+.5m(omega)^2x^2
    and lambda=1 which mean ita a full perturbation
  2. jcsd
  3. Dec 11, 2008 #2


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    In QM, "energy spectrum" is just a stupid word that they use to mean the set of possible energy eigenvalues. I personally hate that terminology; it's so misleading.

    I don't know what this means.
  4. Dec 11, 2008 #3
    haha obviously I agree with you and I read that the lambda in the equation for H=Ho+(lambda)H' when equals to zero means its an unperturbed equation and when it is equal to 1 then its fully perturbed. I dont know I read it.
    But I guess my next question how many energy eigenvalues are there? Does that mean I should probably only go to the second oreder corrections?
  5. Dec 12, 2008 #4


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    How many eigenvalues are there for H0? Can the perturbation remove or add any, or does it just shift them?
  6. Nov 13, 2010 #5
    Sorry, I could say that book is the question?. thank you.
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