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# DREXEL PHYS 516 - Hydrogenic radial plots

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> ### Prof.R. Gilmore Quantum Mechanics 1: > ### Constructs the normalized hydrogen radial wavefunctions> ### Under (int(RX(n,l,r)*R(n,l,r)*r^2,r=0..infinity)=1> ### Plots of radial wavefunctions. Note how scales change!> > > > restart;> with(orthopoly); with(plots); ### calls in useful orthog polys, like the LaguerresG, H, L, P, T, U[ ]Warning, the name changecoords has been redefined[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, cylinderplot, densityplot, display, display3d, fieldplot, fieldplot3d, gradplot, gradplot3d, graphplot3d, implicitplot, implicitplot3d, inequal, interactive, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, odeplot, pareto, plotcom pare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, replot, rootlocus, semilogplot, setoptions, setoptions3d, spacecurve, sparsem atrixplot, sphereplot, surfdata, textplot, textplot3d, tubeplot]> L(5,x); ### for example, it works1 - 5 x + 5 x2 - 53 x3 + 524 x4 - 1120 x5> g(5,0,x):=L(5,x); ### begins process for computing Associated Laguerrspolysg 5, 0, x( ) := 1 - 5 x + 5 x2 - 53 x3 + 524 x4 - 1120 x5> for i from 1 to 7 do g(5,i,x):=diff(g(5,i-1,x),x):print(5,i-1,g(5,i-1,x)):od: #(it works)5, 0, 1 - 5 x + 5 x2 - 53 x3 + 524 x4 - 1120 x55, 1, -5 + 10 x - 5 x2 + 56 x3 - 124 x45, 2, 10 - 10 x + 52 x2 - 16 x35, 3, -10 + 5 x - 12 x25, 4, 5 - x5, 5, -15, 6, 0> for j from 0 to 12 do g(j,0,x):=L(j,x);for i from 1 to j+2 do g(j,i,x):=diff(g(j,i-1,x),x):od:od:## Lots of assoc lag.> for n from 1 to 5 do for l from 0 to n-1 do R(n,l,x):= g(n+l,2*l+1,x)*exp(-x/2)*(x)^l:RR(n,l,r):=subs(x=2*r/n,%):N(n,l):=int(r^2*RR(n,l,r)^2,r=0..infinity):RX(n,l,r):=RR(n,l,r)/sqrt(N(n,l));print(n,l,RX(n,l,r)):od:od: ### constructs normalized hydrogenic radial wavefunctions1, 0, -2 e-r( )2, 0, 14 -2 + r( ) e- 12 ræèöø 22, 1, - 112 e- 12 ræèöø r 63, 0, 227 -3 + 2 r - 29 r2æçèö÷ø e- 13 ræèöø 33, 1, 181 -4 + 23 ræçèö÷ø e- 13 ræèöø r 63, 2, - 21215 e- 13 ræèöø r2 304, 0, 116 -4 + 3 r - 12 r2 + 148 r3æçèö÷ø e- 14 ræèöø4, 1, 1480 -10 + 52 r - 18 r2æçèö÷ø e- 14 ræèöø r 154, 2, 11920 -6 + 12 ræçèö÷ø e- 14 ræèöø r2 54, 3, - 126880 e- 14 ræèöø r3 355, 0, 2125 -5 + 4 r - 45 r2 + 475 r3 - 21875 r4æçèö÷ø e- 15 ræèöø 55, 1, 11875 -20 + 6 r - 1225 r2 + 4375 r3æçèö÷ø e- 15 ræèöø r 305, 2, 265625 -21 + 145 r - 225 r2æçèö÷ø e- 15 ræèöø r2 705, 3, 1328125 -8 + 25 ræçèö÷ø e- 15 ræèöø r3 705, 4, - 24921875 e- 15 ræèöø r4 70> plot({-RX(1,0,r),-RX(2,0,r),-RX(3,0,r),-RX(4,0,r),-RX(5,0,r)},r=0..10); ### s states> plot({-RX(2,1,r),-RX(3,1,r),-RX(4,1,r),-RX(5,1,r)},r=0..15); ### p states> plot({-RX(3,2,r),-RX(4,2,r),-RX(5,2,r)},r=0..35); ### d states> plot({-RX(4,3,r),-RX(5,3,r)},r=0..50); ### f states> plot({-RX(5,4,r)},r=0..75); ### g states> plot({RX(1,0,r)^2,RX(2,0,r)^2,RX(3,0,r)^2,RX(4,0,r)^2,RX(5,0,r)^2},r=0..10); ### s states> plot({RX(2,1,r)^2,RX(3,1,r)^2,RX(4,1,r)^2,RX(5,1,r)^2},r=0..15); ### pstates> plot({RX(3,2,r)^2,RX(4,2,r)^2,RX(5,2,r)^2},r=0..35); ### d states> plot({RX(4,3,r)^2,RX(5,3,r)^2},r=0..50); ### f states> plot({RX(5,4,r)^2},r=0..75); ### g

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