In[]:=
a=20*10^-9;​​h=a/20;​​m=0.067*9.1*10^-31;​​hcutsq=((6.626*10^-34)/(2*3.1416))^2;​​A={​​{((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},​​{1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},​​{0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},​​{0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},​​{0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0},​​{0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0,0,0,0,0,0,0,0,0},​​{0,0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0,0,0,0,0,0,0,0},​​{0,0,0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0,0,0,0,0,0,0},​​{0,0,0,0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0,0,0,0,0,0},​​{0,0,0,0,0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0,0,0,0,0},​​{0,0,0,0,0,0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0,0,0,0},​​{0,0,0,0,0,0,0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0,0,0},​​{0,0,0,0,0,0,0,0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0,0},​​{0,0,0,0,0,0,0,0,0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0,0},​​{0,0,0,0,0,0,0,0,0,0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0,0},​​{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0,0},​​{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1,0},​​{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2,1},​​{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,((h^2)*(2*m*X/hcutsq))-2}};​​MatrixForm[A,TableSpacing{1,1}]​​Det[A];​​B=Solve[Det[A]==0,X];​​E1=(N[EL1=Part[B,1];L1=X/.EL1])/(1.6*10^-22)​​E2=(N[EL2=Part[B,2];L2=X/.EL2])/(1.6*10^-22)​​E3=(N[EL3=Part[B,3];L3=X/.EL3])/(1.6*10^-22)​​E4=(N[EL4=Part[B,4];L4=X/.EL4])/(1.6*10^-22)​​E5=(N[EL5=Part[B,5];L5=X/.EL5])/(1.6*10^-22)​​E1exact=(hcutsq/(2*m))*((1*Pi/a)^2)/(1.6*10^-22)​​E2exact=(hcutsq/(2*m))*((2*Pi/a)^2)/(1.6*10^-22)​​E3exact=(hcutsq/(2*m))*((3*Pi/a)^2)/(1.6*10^-22)​​E4exact=(hcutsq/(2*m))*((4*Pi/a)^2)/(1.6*10^-22)​​E5exact=(hcutsq/(2*m))*((5*Pi/a)^2)/(1.6*10^-22)​​
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Out[]=
-4621.58
Out[]=
-1231.51
Out[]=
-869.209
Out[]=
-504.838
Out[]=
-385.284
Out[]=
14.0642