Using Dsolve in mathematica

0
votes

I was using dsolve to find the solved differential equation for the Schrodinger equations involving magnetic resonance and i am getting an error. 

DSolve[{I*a'[t] == .5*(w0*a[t] + w1*Cos[w*t]*b[t]), 

 I*b'[t] == .5*(w1*Cos[w*t]*a[t] - w0*b[t]), 

a[t]^2 + b[t]^2 == 1}, {a, b}, t]

from this i am getting the reply

There are fewer dependent variables than equations, so the system is \

overdetermined.

i see 3 equation and 3 unknowns so i do not really know why it is doing this. Any help would be appreciated.

1
wolfram-mathematicadsolve
you have two unknown functions a,b. (?) - agentp

1 Answers

0
votes

Perhaps this will help.

Ref. NMR Transition Rate in a Oscillating B Field

enter image description here

DSolve[
  b'[t] == ((I w1)/2) (Exp[I (w + w0) t] + Exp[-I (w - w0) t]) - I w0 b[t],
  b[t], t] // Simplify

enter image description here