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with(IntegrationTools):with(Physics):
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h1 := (m,n)->(n+1/2)*KroneckerDelta[n,m];
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![proc (m, n) options operator, arrow; Physics:-`*`(n+Physics:-`*`(1, Physics:-`^`(2, -1)), Physics:-KroneckerDelta[n, m]) end proc](/view.aspx?sf=236588_question/929aec4fcbf328dba66abca43175806e.gif)
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(1) |
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h2 := (mu,nu,m2,l)->-(nu*Pi/l)^2/(2*m2)*KroneckerDelta[mu,nu];
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![proc (mu, nu, m2, l) options operator, arrow; Physics:-`*`(-1, Physics:-`*`(Physics:-`^`(Physics:-`*`(nu, Pi, Physics:-`^`(l, -1)), 2), Physics:-`^`(Physics:-`*`(2, m2), -1), Physics:-KroneckerDelta[mu, nu])) end proc](/view.aspx?sf=236588_question/576295d21cddd5756ec114f07b5e2ba2.gif)
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(2) |
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v1 := (m,n,m1)->sqrt(min(n,m)!/max(n,m)!)*(2*m1)^(-abs(n-m)/2)*exp(-1/(4*m1))*LaguerreL(min(n,m),abs(n-m),-1/(2*m1));
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(3) |
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v2 := (mu,nu,l)->4*Pi^2*l*mu*nu*(exp(l/2)-(-1)^(mu+nu)*exp(-l/2))/((Pi*(mu+nu))^2+l^2)/((Pi*(mu-nu))^2+l^2);
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(4) |
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h:=(m,n,mu,nu,m1,m2,l)->evalf(h1(m,n)+h2(mu,nu,m2,l)+v1(m,n,m1)+v2(mu,nu,l));
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(5) |
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H:= (m,n,mu,nu)->h(m,n,mu,nu,m1,m2,l);
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(6) |
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(7) |
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eq1:= diff(z(m,nu,t),t)=-I*Sum(Sum(H(m,n,mu,nu)*z(n,mu,t),n=1..N),mu=0..M);
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![diff(z(m, nu, t), t) = -I*(Sum(Sum(((n+.5000000000)*Physics:-KroneckerDelta[m, n]-4.934802202*nu^2*Physics:-KroneckerDelta[mu, nu]+.7788007831*(factorial(min(m, n))/factorial(max(m, n)))^(1/2)*2.^(-.5000000000*abs(-1.*n+m))*LaguerreL(min(m, n), abs(-1.*n+m), -.5000000000)+39.47841762*mu*nu*(1.648721271-.6065306597*(-1.)^(mu+nu))/((9.869604404*(mu+nu)^2+1.)*(9.869604404*(mu-1.*nu)^2+1.)))*z(n, mu, t), n = 1 .. N), mu = 0 .. M))](/view.aspx?sf=236588_question/79252bee2910d84b1521acf2efbc3fdd.gif)
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(8) |
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zint := Array([[1,0],[0,1]]);
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(9) |
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Z:= Array(1..2,1..2);
for i from 1to 2 do
for j from 1 to 2 do
Z[i,j]:= dsolve({eq1,zint[i,j]},numeric,output=listprocedure);
end do;
end do;
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