作者tingting88 ()
看板Physics
标题[问题] Bohr-Sommerfeld quantization rule
时间Fri May 8 17:38:03 2009
[领域] Quantum Mechanics
[题目] 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
[瓶颈] 我会列式但是积不出来
我後来的方程式是:
1 2E
∫ [1-y^2-ε^2──y^4]^0.5 dy
-1 hω
有没有高手知道要怎麽变数变换或者近似才能凑出题目中给的积分式?
谢谢!
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