Re: [透客] 見見世面吧！（誤）（傳教）

[bwlaq (洞庭波兮木葉下)]

我只選出大家不會的XD  (p.s.:這是普化)

4.For a particle in a 2-dimensional box,the energy and the wave function are
  given as:

L ┌───┐
  │      │
 y│ V=0  │   V=無限大
  │      │
  └───┘
0     x    L


E(nx,ny)=(nx^2+ny^2) h^2/(8mL^2)

                2      nxπx      nyπy
ψ      (x,y)=(-─)sin(───)sin(───)      ( nx,ny=1,2,3,... )
  nx ny         L        L          L

Please answer the follwing questions:
a)The zero point energy;
b)The wave funtion ψ    (x,y)and the energy E(2,2)
                     2,2
c)The wave funtion ψ    (x,y)and the energy E(3,1)
                     3,1
d)The wave function with the zero point energy
e)Areψ    (x,y)andψ    (x,y) degenerate?            (10pts)
       2,2           3,1


這還是簡單的，代數字就有答案

再來一題

10.A wave function of hydrogen atomic orbritals is given as:

        1        1  5/2   -r/2a0                         o
ψ= ───── (-─)    re       sinθcosφ   (a0 = 0.529A,Bohr radius)
    4(2π)^1/2   a0

a)Please calculatepositions of nodal surfaces;
b)Give a pictorial drawing of ψ including nodal surfaces;
c)Convert ψ into a function of ψ(x,y,z);
d)What is the symbol of atomic orbrital(eg:1s,2pz,3dz^2)?   (10PTS)


這還不是最難的，最難的是這題

11.The wave funtion of the hydroden 1s atomic orbrital is given as:

         1    1  3/2  -r/a0                   o
  ψ  = ── (─)    e             (a0 = 0.529A,Bohr radius)
    1s  π^2  a0

  The probability function of the 1s atomic orbrital is P1s(r)=4πr^2[ψ1s]^2
  and the maximum probability (or electron density) of finding the electron is
  at  d[P1s(r)]
     ───── = 0 .
         dr
  Please calculate the position of maximum electron density.  (6PTS)




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