### 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 restart; with(orthopoly); ### calls in useful orthog polys, like the Laguerres NiM3KEkiR0c2IkkiSEdGJUkiTEdGJUkiUEdGJUkiVEdGJUkiVUdGJQ== L(5,x); ### for example, it works NiMsLiIiIkYkSSJ4RzYiISImKiRGJSIiIyIiJiokRiUiIiQjRidGLCokRiUiIiUjRioiI0MqJEYlRiojISIiIiQ/Ig== g(5,0,x):=L(5,x); ### begins process for computing Associated Laguerrs polys NiM+LUkiZ0c2IjYlIiImIiIhSSJ4R0YmLC4iIiJGLEYqISImKiRGKiIiI0YoKiRGKiIiJCNGLUYxKiRGKiIiJSNGKCIjQyokRipGKCMhIiIiJD8i 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) NiUiIiYiIiEsLiIiIkYmSSJ4RzYiISImKiRGJyIiI0YjKiRGJyIiJCNGKUYtKiRGJyIiJSNGIyIjQyokRidGIyMhIiIiJD8i NiUiIiYiIiIsLCEiJkYkSSJ4RzYiIiM1KiRGJyIiI0YmKiRGJyIiJCNGIyIiJyokRiciIiUjISIiIiND NiUiIiYiIiMsKiIjNSIiIkkieEc2IiEjNSokRihGJCNGI0YkKiRGKCIiJCMhIiIiIic= NiUiIiYiIiQsKCEjNSIiIkkieEc2IkYjKiRGKCIiIyMhIiJGKw== NiUiIiYiIiUsJkYjIiIiSSJ4RzYiISIi NiUiIiZGIyEiIg== NiUiIiYiIiciIiE= for j from 0 to 10 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 aqssoc 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 wavefunctions NiUiIiIiIiEsJC1JJGV4cEc2JEkqcHJvdGVjdGVkR0YpSShfc3lzbGliRzYiNiMsJEkickdGKyEiIiEiIw== NiUiIiMiIiEsJCooLCYhIiMiIiJJInJHNiJGKUYpLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRi9JKF9zeXNsaWJHRis2IywkRiojISIiRiNGKUYjI0YpRiMjRikiIiU= NiUiIiMiIiIsJCooLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRipJKF9zeXNsaWJHNiI2IywkSSJyR0YsIyEiIkYjRiRGL0YkIiInI0YkRiMjRjEiIzc= NiUiIiQiIiEsJCooLCghIiQiIiJJInJHNiIiIiMqJEYqRiwjISIjIiIqRiktSSRleHBHNiRJKnByb3RlY3RlZEdGNEkoX3N5c2xpYkdGKzYjLCRGKiMhIiJGI0YpRiMjRilGLCNGLCIjRg== NiUiIiQiIiIsJCoqLCYhIiVGJEkickc2IiMiIiNGI0YkLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRjBJKF9zeXNsaWJHRio2IywkRikjISIiRiNGJEYpRiQiIicjRiRGLCNGJCIjIik= NiUiIiQiIiMsJCooLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRipJKF9zeXNsaWJHNiI2IywkSSJyR0YsIyEiIkYjIiIiRi9GJCIjSSNGMkYkIyEiIyIlOjc= NiUiIiUiIiEsJComLCohIiUiIiJJInJHNiIiIiQqJEYqIiIjIyEiIkYuKiRGKkYsI0YpIiNbRiktSSRleHBHNiRJKnByb3RlY3RlZEdGN0koX3N5c2xpYkdGKzYjLCRGKiNGMEYjRikjRikiIzs= NiUiIiUiIiIsJCoqLCghIzVGJEkickc2IiMiIiYiIiMqJEYpRi0jISIiIiIpRiQtSSRleHBHNiRJKnByb3RlY3RlZEdGNUkoX3N5c2xpYkdGKjYjLCRGKSNGMEYjRiRGKUYkIiM6I0YkRi0jRiQiJCFb NiUiIiUiIiMsJCoqLCYhIiciIiJJInJHNiIjRilGJEYpLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRjBJKF9zeXNsaWJHRis2IywkRiojISIiRiNGKUYqRiQiIiZGLCNGKSIlPz4= NiUiIiUiIiQsJCooLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRipJKF9zeXNsaWJHNiI2IywkSSJyR0YsIyEiIkYjIiIiRi9GJCIjTiNGMiIiIyNGMSImISlvIw== NiUiIiYiIiEsJCooLCwhIiYiIiJJInJHNiIiIiUqJEYqIiIjIyEiJUYjKiRGKiIiJCNGLCIjdiokRipGLCMhIiMiJXY9RiktSSRleHBHNiRJKnByb3RlY3RlZEdGPEkoX3N5c2xpYkdGKzYjLCRGKiMhIiJGI0YpRiMjRilGLiNGLiIkRCI= NiUiIiYiIiIsJCoqLCohIz9GJEkickc2IiIiJyokRikiIiMjISM3IiNEKiRGKSIiJCMiIiUiJHYkRiQtSSRleHBHNiRJKnByb3RlY3RlZEdGOUkoX3N5c2xpYkdGKjYjLCRGKSMhIiJGI0YkRilGJCIjSSNGJEYtI0YkIiV2PQ== NiUiIiYiIiMsJCoqLCghI0AiIiJJInJHNiIjIiM5RiMqJEYqRiQjISIjIiNERiktSSRleHBHNiRJKnByb3RlY3RlZEdGNUkoX3N5c2xpYkdGKzYjLCRGKiMhIiJGI0YpRipGJCIjcSNGKUYkI0YkIiZEYyc= NiUiIiYiIiQsJCoqLCYhIikiIiJJInJHNiIjIiIjRiNGKS1JJGV4cEc2JEkqcHJvdGVjdGVkR0YxSShfc3lzbGliR0YrNiMsJEYqIyEiIkYjRilGKkYkIiNxI0YpRi0jRikiJ0QiRyQ= NiUiIiYiIiUsJCooLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRipJKF9zeXNsaWJHNiI2IywkSSJyR0YsIyEiIkYjIiIiRi9GJCIjcSNGMiIiIyMhIiMiKHY9I1w= for n from 1 to 5 do for l from 0 to n-1 do print(n,l,RX(n,l,r)):od:od: NiUiIiIiIiEsJC1JJGV4cEc2JEkqcHJvdGVjdGVkR0YpSShfc3lzbGliRzYiNiMsJEkickdGKyEiIiEiIw== NiUiIiMiIiEsJCooLCYhIiMiIiJJInJHNiJGKUYpLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRi9JKF9zeXNsaWJHRis2IywkRiojISIiRiNGKUYjI0YpRiMjRikiIiU= NiUiIiMiIiIsJCooLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRipJKF9zeXNsaWJHNiI2IywkSSJyR0YsIyEiIkYjRiRGL0YkIiInI0YkRiMjRjEiIzc= NiUiIiQiIiEsJCooLCghIiQiIiJJInJHNiIiIiMqJEYqRiwjISIjIiIqRiktSSRleHBHNiRJKnByb3RlY3RlZEdGNEkoX3N5c2xpYkdGKzYjLCRGKiMhIiJGI0YpRiMjRilGLCNGLCIjRg== NiUiIiQiIiIsJCoqLCYhIiVGJEkickc2IiMiIiNGI0YkLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRjBJKF9zeXNsaWJHRio2IywkRikjISIiRiNGJEYpRiQiIicjRiRGLCNGJCIjIik= NiUiIiQiIiMsJCooLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRipJKF9zeXNsaWJHNiI2IywkSSJyR0YsIyEiIkYjIiIiRi9GJCIjSSNGMkYkIyEiIyIlOjc= NiUiIiUiIiEsJComLCohIiUiIiJJInJHNiIiIiQqJEYqIiIjIyEiIkYuKiRGKkYsI0YpIiNbRiktSSRleHBHNiRJKnByb3RlY3RlZEdGN0koX3N5c2xpYkdGKzYjLCRGKiNGMEYjRikjRikiIzs= NiUiIiUiIiIsJCoqLCghIzVGJEkickc2IiMiIiYiIiMqJEYpRi0jISIiIiIpRiQtSSRleHBHNiRJKnByb3RlY3RlZEdGNUkoX3N5c2xpYkdGKjYjLCRGKSNGMEYjRiRGKUYkIiM6I0YkRi0jRiQiJCFb NiUiIiUiIiMsJCoqLCYhIiciIiJJInJHNiIjRilGJEYpLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRjBJKF9zeXNsaWJHRis2IywkRiojISIiRiNGKUYqRiQiIiZGLCNGKSIlPz4= NiUiIiUiIiQsJCooLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRipJKF9zeXNsaWJHNiI2IywkSSJyR0YsIyEiIkYjIiIiRi9GJCIjTiNGMiIiIyNGMSImISlvIw== NiUiIiYiIiEsJCooLCwhIiYiIiJJInJHNiIiIiUqJEYqIiIjIyEiJUYjKiRGKiIiJCNGLCIjdiokRipGLCMhIiMiJXY9RiktSSRleHBHNiRJKnByb3RlY3RlZEdGPEkoX3N5c2xpYkdGKzYjLCRGKiMhIiJGI0YpRiMjRilGLiNGLiIkRCI= NiUiIiYiIiIsJCoqLCohIz9GJEkickc2IiIiJyokRikiIiMjISM3IiNEKiRGKSIiJCMiIiUiJHYkRiQtSSRleHBHNiRJKnByb3RlY3RlZEdGOUkoX3N5c2xpYkdGKjYjLCRGKSMhIiJGI0YkRilGJCIjSSNGJEYtI0YkIiV2PQ== NiUiIiYiIiMsJCoqLCghI0AiIiJJInJHNiIjIiM5RiMqJEYqRiQjISIjIiNERiktSSRleHBHNiRJKnByb3RlY3RlZEdGNUkoX3N5c2xpYkdGKzYjLCRGKiMhIiJGI0YpRipGJCIjcSNGKUYkI0YkIiZEYyc= NiUiIiYiIiQsJCoqLCYhIikiIiJJInJHNiIjIiIjRiNGKS1JJGV4cEc2JEkqcHJvdGVjdGVkR0YxSShfc3lzbGliR0YrNiMsJEYqIyEiIkYjRilGKkYkIiNxI0YpRi0jRikiJ0QiRyQ= NiUiIiYiIiUsJCooLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRipJKF9zeXNsaWJHNiI2IywkSSJyR0YsIyEiIkYjIiIiRi9GJCIjcSNGMiIiIyMhIiMiKHY9I1w= for n from 1 to 5 do for l from 1 to n-1 do over(n,l):=int(RX(n,l,r)*RX(n,l-1,r)*r*r^2,r=0..infinity):print(n,l,over(n,l)):od:od: NiUiIiMiIiIsJCokIiIkI0YkRiMhIiQ= NiUiIiQiIiIsJCokIiIjI0YkRichIio= NiUiIiQiIiMsJCokIiImIyIiIkYkIyEiKkYk NiUiIiUiIiIsJCokIiM6I0YkIiIjISIn NiUiIiUiIiMsJCokIiIkIyIiIkYkISM3 NiUiIiUiIiQsJCokIiIoIyIiIiIiIyEiJw== NiUiIiYiIiIsJCokIiInI0YkIiIjISM6 NiUiIiYiIiMsJComIiIoIyIiIkYkIiIkRigjISM6RiQ= NiUiIiYiIiQhI0k= NiUiIiYiIiUjISNYIiIj