Pimag.Dir , OUTPUT FILE NAME

Ground State pimag.dir , OUTPUT FILE NAME "p.out 1 3", DATA SET NAME 1,1 dimension of X in FA(X), NPOW in ((f-fA)/err)**(2*NPOW) C,1E-4,0,1E-2 'R' read data point,err, 'C' err=(a+bf)^.5 +c 19 total number of constants (ones with vary 0 are not being f 2000, maximum number of minimization steps 0.99,Pen,2 2e0,abs, initial fr, Penalty-if all caps-,Npen Ala 1 VARY O FIX FITTED CONS ERROR IN CONS 0 -2.3654186379415446E-17 +- 0.000 1 -1.0292638984335221E+00 +- 1.046E-03 0 3.2963332438101381E-18 +- 0.000 1 9.7979259953240749E-02 +- 3.150E-04 0 0.0000000000000000E+00 +- 0.000 1 -4.8862367624436945E-03 +- 2.696E-05 0 0.0000000000000000E+00 +- 0.000 1 8.7061551633673838E-05 +- 6.719E-07 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 ended because abs(chb-chl)/chl<1e-9 CHI,CHIPEN= 1644. 0.0000 FOR 2002 DATA POINTS CHI USED IN CALCULATING ERRORS IS 1998. SUM ((FA-F)/EP)**2 = 1644.1093519463358916 NDAT = 2002 Figure 1 Fit to pimag preal.dir , OUTPUT FILE NAME p.out, DATA SET NAME 1,1 dimension of X in FA(X), NPOW in ((f-fA)/err)**(2*NPOW) C,1E-4,0,1e-4 'R' read data point,err, 'C' err=(a+bf)^.5 +c*abs 23 total number of constants (ones with vary 0 are not being f 2000, maximum number of minimization steps 0.99,Pen,2 2e0,abs, initial fr, Penalty-if all caps-,Npen Ala 1 VARY O FIX FITTED CONS ERROR IN CONS 1 -4.8131448022765040E-02 +- 1.606E-03 0 -8.1804848619958002E-20 +- 0.000 1 1.3894271857304943E-01 +- 1.284E-03 0 5.2782253766458318E-19 +- 0.000 1 4.0867753776578530E-02 +- 2.516E-04 0 0.0000000000000000E+00 +- 0.000 1 -2.0572737510875395E-03 +- 1.688E-05 0 0.0000000000000000E+00 +- 0.000 1 3.4753502608072394E-05 +- 3.607E-07 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 0 0.0000000000000000E+00 +- 0.000 ended because abs(chb-chl)/chl<1e-9 CHI,CHIPEN= 1.6930E+04 0.0000 FOR 2002 DATA POINTS CHI USED IN CALCULATING ERRORS IS 0.1693E+05 SUM ((FA-F)/EP)**2 = 16929.6526084568940860 NDAT = 2002

Figure 2 fit to preal Ext.bat EulerExt

Figure 3 P(x) across entire region Figure 4 exp(-p(x))

The sum exp(-p(x))+exp(p(x)) will cancel the imaginary part of the wave function.

First excited state EH = -3.238 Figure 5 First Excited state

Figure 6 exp(-p(x))

The real part of this wave function is cancelled in Psi(x)=exp(-p(x))-exp(p(x)). 2nd Excited state

EH=-2.14

3rd State

EH=-1.04 First Resonance

EH = 0.6 X'S FOR E=POT(X)- 0.6000000000000000

-10.3682816720244215 -3.2450375479612377 3.2450375479612377 10.3682816720244215

The differential equation has trouble in the region where p should expand to catch the plane waves to the right and left. In the bound region, this is just another bound state.

Figure 7 Expanded view near the end of the convergence region.

Starting at 30 and working down towards 10 p is easily found The two wave functions in this region are exp(-p(x)) and exp(+p(x)). In the case of scattering the exp(+p(x)) does not exist in this region.