/* Symbolic checks for Modern Physics Unit II.
   Run: maxima --very-quiet -b molecular-radioactivity.mac */
kill(all)$
display2d:false$

Nplus : 1/sqrt(2*(1+S))$
Nminus : 1/sqrt(2*(1-S))$
print("bonding-orbital normalization residual =",
      ratsimp(Nplus^2*2*(1+S)-1))$
print("antibonding-orbital normalization residual =",
      ratsimp(Nminus^2*2*(1-S)-1))$

F(J) := B*J*(J+1)$
print("rigid-rotor line-position residual =",
      ratsimp(F(J+1)-F(J)-2*B*(J+1)))$
print("rigid-rotor adjacent-spacing residual =",
      ratsimp((F(J+2)-F(J+1))-(F(J+1)-F(J))-2*B))$

G(v) := hbar*omega*(v+1/2)$
print("harmonic-vibration spacing residual =",
      ratsimp(G(v+1)-G(v)-hbar*omega))$

Ndecay(t) := N0*exp(-lambda*t)$
print("radioactive-decay differential residual =",
      ratsimp(diff(Ndecay(t),t)+lambda*Ndecay(t)))$
print("half-life residual =",
      ratsimp(subst(log(2)/lambda,t,Ndecay(t))/N0-1/2))$

assume(lambda>0)$
mean_num : integrate(t*lambda*exp(-lambda*t),t,0,inf)$
mean_den : integrate(lambda*exp(-lambda*t),t,0,inf)$
print("mean-life residual =",
      ratsimp(mean_num/mean_den-1/lambda))$

quit()$