Review schrodinger equations not dependent on 3D time in ball coordinates v² + V(F) )p(F) = E Þ(F) 2m With = (r, 0,9) and E is the energy system. Assume the potential is only radial function V(*) = V(r) To solve the Schrodinger equation above apply the method p(r, 0, q) = R(r)P(0)Q(9) variable separation problem : By defining u(r) = rR(r) where u(r) qualifies the limit of u(0) = 0 and u(--) = Show that fulfilling the radial equation u(r) h? d?u h2 l(1 + 1) +V(r) + 2m u = E u 2m dr2 r2
Review schrodinger equations not dependent on 3D time in ball coordinates v² + V(F) )p(F) = E Þ(F) 2m With = (r, 0,9) and E is the energy system. Assume the potential is only radial function V(*) = V(r) To solve the Schrodinger equation above apply the method p(r, 0, q) = R(r)P(0)Q(9) variable separation problem : By defining u(r) = rR(r) where u(r) qualifies the limit of u(0) = 0 and u(--) = Show that fulfilling the radial equation u(r) h? d?u h2 l(1 + 1) +V(r) + 2m u = E u 2m dr2 r2
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Transcribed Image Text:Review schrodinger equations not dependent on 3D time in ball coordinates
(
v² +V(f) )v(F) = E Þ(*)
2m
With = (r, 0, 9) and E is the energy system. Assume the potential is only radial function
V(*) = V(r) To solve the Schrodinger equation above apply the method
p(r, 0, q) = R(r)P(0)Q(9)
variable separation
problem : By defining u(r) = rR(r) where u(r) qualifies the limit of u(0) = 0 and u(--) = Show that
fulfilling the radial equation u(r)
h? d?u
h? l(l + 1)
+(V(r) +
2m
u = Eu
2m dr2
r2
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