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

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Below is the EigenEnergy obtained in part a 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 0.0833333 1.08333 0.47619 1.47619 Gen the truncated H-Matrix with dimension=dim and find the eigen value f @ Α _, Β _, Γ _,dim_ D : = Module B8< , H @ m_,n_ D : = n - 1 + 1 2 KroneckerDelta @ m - 1,n - 1 D + Α H n + 1 L H n L KroneckerDelta @ m - 1,n + 1 D - Α H n - 1 L H n - 2 L KroneckerDelta @ m - 1,n - 3 D + Β + Γ 2 n KroneckerDelta @ m - 1,n D + Β - Γ 2 n - 1 KroneckerDelta @ m - 1,n - 2 D ; Abs @ Eigenvalues @ Array @ H, 8 dim,dim <DDD FH * end Module * L Some Example: f @ 0.1,1.,1.,20 D 8 27.3823,22.9543,19.6719,17.0698,15.0041,13.4896,12.4481,11.4334,10.4352,9.45504, 8.47477,7.49493,6.51514,5.53534,4.55554,3.57575,2.59595,1.61616,0.636361,0.343435 < f @ 10.,1.,1.,20 D 8 314.42156086691807`,290.6560848911792`,277.2102620494352`,260.8022482671494`, 208.5985343967945`,188.32743259513072`,179.1702493174536`,164.98097196450402`, 132.79240299145147`,115.60638609244246`,109.33926913742935`,97.24786919103833`, 74.84357479386493`,60.84880754820452`,56.323576074685846`,46.77494771272922`, 28.90610724678387`,20.109630934604308`,13.948808898115635`,9.312319744834639` < 8 314.422,290.656,277.21,260.802,208.599,188.327,179.17,164.981,132.792,115.606, 109.339,97.2479,74.8436,60.8488,56.3236,46.7749,28.9061,20.1096,13.9488,9.31232 < Approx. Ground State Energy for Α =0.1, which shows a fast converge Table @ Last @ f @ 0.1,1.,1.,i DD , 8 i,4,20,2 <D 8 0.33983,0.343399,0.343435,0.343435,0.343435,0.343435,0.343435,0.343435,0.343435 < Approx. 1st Excited State Energy for Α =0.1, which shows a fast converge

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Table @ Part @ f @ 0.1,1.,1.,i D , -
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HW2.1 - Below is the EigenEnergy obtained in part a 1 1 2 2...

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