1.Consider a modified version of the 1D particle-in-a-box problem：
  a slight change to square-well potential is made in such a way that there
  now exists a "trap" of width "a" and depth "-ε" at the center of the well
  ofinfinite depth(cf. Figure1 )

 (1)On the basis of the perturbation theory,derive expression for the
    1st-order correction to the ground state and the first excited state
    energies.Note that,in the absence of the trap,the "unpertured"
    wavefunction are of the form Ψn(x)=(2/L)^(1/2) sin(nπx/L) with
    corresponding energies En= (nh)^2/8mL^2 for 0<x<L and n=1,2,3....

 (2)Show that the ground-state energy is always negative(i.e. the ground-state
    wavefunction is more or less confined in the shallow trap),no matter how
    the trap is.

    ∞                ∞
    ↑                ↑      ps.抱歉 圖畫得很爛@@
    │                │         題目的意思好像是是一個1D盒子裡有個長度a 深度
    │                │         ε的trap
    │     ← a →    │
   0└──┼    ┼──┘
          └──┘-ε
     ←──  L  ───→



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