Definition at line 95 of file numerov_solve.py. 00095 : 00096 "generate a candidate eigenfunction with given potential, assuming the potential well has a single allowed region bounded on both sides" 00097 assert len(V0) & 1, "Must have a grid with an odd number of points" 00098 vminchan=Numeric.argmin(V0) #position of bottom of well 00099 right_turn=Numeric.searchsorted(V0[vminchan:], 0.0)+vminchan #position of right-hand turning point 00100 00101 #integrate from left end to right-hand turning point, at which point numerov method becomes unstable 00102 leftpsi=bare_numerov(V0[:right_turn], dx) 00103 #iterate backwards on right part to turning point, and flatten to normal array 00104 rightpsi= Numeric.array(bare_numerov(V0[right_turn-overlapsize:][::-1], dx)[::-1]) 00105 00106 #remember that since Numeric handles slices without copying, leftend and rightend also scale here 00107 slopeweight=Numeric.array(range(overlapsize),Numeric.Float)-overlapsize/2.0 00108 leftend=leftpsi[-overlapsize:] 00109 rightend=rightpsi[:overlapsize] 00110 00111 scale=abs(Numeric.sum(leftend*rightend)/Numeric.sum(leftend**2)) #'least-squares' scale estimate 00112 #note that since leftend and rightend are Numeric slice references, modifying psi also changes them! 00113 rightpsi*=float(parity)/scale 00114 error=Numeric.sum((leftend-rightend)*slopeweight) #average derivative 00115 psi0=Numeric.concatenate((leftpsi, rightpsi[overlapsize:])) 00116 00117 psi2=psi0*psi0 00118 integral=psi2[0]+psi2[-1]+4.0*Numeric.sum(psi2[1:-1:2])+2.0*Numeric.sum(psi2[2:-2:2]) #use simpson's rule 00119 psimag=1.0/math.sqrt(integral*dx/3.0) 00120 00121 return psi0*psimag, error*psimag 00122 def single_well_numerov_solve(V0, dx, parity, emin, emax, overlapsize=5):
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1.5.4