# HW2 - Below is the EigenEnergy obtained in part a 1 1 2 2...

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Below is the EigenEnergy obtained in part a In[97]:= Energy @ n_, Α _, Β _, Γ _ D : = n + 1 2 - 1 2 Β 2 + Γ 2 - 4 Α Β Γ 2 I 1 - 4 Α 2 M ; Energy @ 0, 0.1, 1, 1 DH * Α= 0.1 Ground State * L Energy @ 1, 0.1, 1, 1 DH * Α= 0.1 1st Excited State * L Energy @ 0, 10., 1, 1 DH * Α= 10 Ground State * L Energy @ 1, 10., 1, 1 DH * Α= 10 1st Excited State * L Out[98]= 0.0833333 Out[99]= 1.08333 Out[100]= 0.47619 Out[101]= 1.47619 Gen the truncated H-Matrix with dimension=dim and find the eigen value In[80]:= f @ Α _, Β _, Γ _, dim_ D : = Module B8< , H @ m_, n_ D : = n + 1 2 KroneckerDelta @ m, n D + ± Α H n + 2 L H n + 1 L KroneckerDelta @ m, n + 2 D - ± Α H n L H n - 1 L KroneckerDelta @ m, n - 2 D + Β + ± Γ 2 n + 1 KroneckerDelta @ m, n + 1 D + Β - ± Γ 2 n KroneckerDelta @ m, n - 1 D ; Abs @ Eigenvalues @ Array @ H, 8 dim, dim <DDD FH * end Module * L Some Example: In[102]:= f @ 0.1, 1., 1., 20 D Out[102]= 8 28.7249, 24.2314, 20.8891, 18.2271, 16.0961, 14.508, 13.4393, 12.4221, 11.4157, 10.4352,

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HW2 - Below is the EigenEnergy obtained in part a 1 1 2 2...

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