[問題] Bohr-Sommerfeld quantization rule

[tingting88 ()]

[領域] Quantum Mechanics

[題目]      p^2    mω^2           hω
        H = ── + ── x^2 + ε^2 ── x^4  where ε<< 1
             2m     2              2λ

        Apply Bohr-Sommerfeld quantization rule to calculate the energy levels.

        The following integral is helpful

         1             dξ                      -a^2           a^2
       ∫  ─────────────── = 2K(───) ≒ π-π──  where a<<1
        -1 [1-(ξ^2+a^2ξ^4)/(1+a^2)]^0.5       1+a^2           4

[瓶頸]  我會列式但是積不出來

        我後來的方程式是:

          1            2E
        ∫ [1-y^2-ε^2──y^4]^0.5 dy
         -1            hω

        有沒有高手知道要怎麼變數變換或者近似才能湊出題目中給的積分式?

        謝謝!

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