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Help with loops in Mathematica (Hamiltonian)

  1. May 6, 2013 #1
    1. The problem statement, all variables and given/known data

    I have an assignment for my thesis to make Hamiltonian for Schrodinger equation. I won't go into physics part of it, because that is well understood.

    I need to somehow generate a specific matrix for Hamiltonian (H).

    Please see the attached file of what I need to get.

    2. Relevant equations

    See attached file

    3. The attempt at a solution

    I have thought of solution for this in C, but I don't know how to syntax this in Mathematica.

    The solution for this in C would be to generate 7x7 matrix where elements (i,j) would be made by:

    If
    i=j
    ΔE
    Else
    If
    i-j=1
    Ω(rf) complex conjugate
    i-j=-1
    Ω(rf)
    Else
    0
     

    Attached Files:

  2. jcsd
  3. May 7, 2013 #2

    DrClaude

    User Avatar

    Staff: Mentor

    The best way I know is to create a 2D table and use KroneckerDelta to decide the value of each element in the table.
     
  4. May 9, 2013 #3
    In[1]:= H = Table[
    Which[
    i == j, g*\[Mu]B*ToExpression["m" <> ToString]*B,
    i - j == 1, Conjugate[\[CapitalOmega]rf],
    i - j == -1, \[CapitalOmega]rf,
    True, 0
    ], {i, 7}, {j, 7}
    ]

    Out[1]= {{B g m1 \[Mu]B, \[CapitalOmega]rf, 0, 0, 0, 0, 0},
    {Conjugate[\[CapitalOmega]rf], B g m2 \[Mu]B, \[CapitalOmega]rf, 0, 0, 0, 0},
    {0, Conjugate[\[CapitalOmega]rf], B g m3 \[Mu]B, \[CapitalOmega]rf, 0, 0, 0},
    {0, 0, Conjugate[\[CapitalOmega]rf], B g m4 \[Mu]B, \[CapitalOmega]rf, 0, 0},
    {0, 0, 0, Conjugate[\[CapitalOmega]rf], B g m5 \[Mu]B, \[CapitalOmega]rf, 0},
    {0, 0, 0, 0, Conjugate[\[CapitalOmega]rf], B g m6 \[Mu]B, \[CapitalOmega]rf},
    {0, 0, 0, 0, 0, Conjugate[\[CapitalOmega]rf], B g m7 \[Mu]B}}
     
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