using System;
using Science.Mathematics;
using L = Science.Physics.QuantumMechanics;
namespace ScienceTest.PhysicsTest.QuantumMechanicsTest
{
///
/// We solve the differential equation : R(r) = r^l \Psi(r)
/// -0.5{\Psi''(r) + (2l+2)/r\Psi'(r)} + V(r)\Psi(r) = E\Psi(r)
///
public class SchroedingerEq3DTest
{
public SchroedingerEq3DTest()
{
}
private string result;
public string Result
{
get{return result;}
}
public void Compute()
{
L.SchroedingerEquation3D equation = new L.SchroedingerEquation3D();
Function.ToLastType func = new Function.ToLastType(V);
equation.PotentialEnergy = func;
equation.CoefficientOfSingularAtOrigin = -1.0;
/* // solution of n=1, that is, E = -0.5/n^2 = -0.5
equation.RadialBoundary = 10.0; // radius should be large enough for wavefunction to be 0
equation.EnergyGuess = -0.57; // change as you wish
equation.SlopeGuess = 227*1.0E-7; // change to adjust \Psi(r)
equation.ValueAtOriginGuess = 1.6; // change as you wish
// solution of n=2, that is, E = -0.5/n^2 = -0.125
equation.RadialBoundary = 60.0;
equation.EnergyGuess = -0.505; // change as you wish
equation.SlopeGuess = -5.0E-10; // change to adjust \Psi(r)
equation.ValueAtOriginGuess = 10.6E-3; // change as you wish
// solution of n=3, that is, E = -0.5/n^2 = -0.055555
equation.RadialBoundary = 60.0;
equation.EnergyGuess = -0.51; // change as you wish
equation.SlopeGuess = 20*5.0E-9; // change to adjust \Psi(r)
equation.ValueAtOriginGuess = 0.005; // change as you wish
*/
// solution of n=4, that is, E = -0.5/n^2 = -0.03125
equation.RadialBoundary = 60.0;
equation.EnergyGuess = -0.51; // change as you wish
equation.SlopeGuess = 138*5.0E-9; // change to adjust \Psi(r)
equation.ValueAtOriginGuess = 0.001; // change as you wish
equation.Solve();
for(int k = 0; k < equation.WaveFunction.Length; k++)
result += Convert.ToString(equation.WaveFunctionRadialCoordinate[k])+"\t" // position
+ Convert.ToString(equation.WaveFunction[k])+"\t" // value
+ Convert.ToString(equation.WaveFunctionDerivative[k])+"\r\n"; // derivative
result += equation.SolvedQ+" Energy="+Convert.ToString(equation.Energy)+"\r\n";
/* for(int k = 100; k < 300; k++)
{
equation.EnergyGuess = -0.57; // change as you wish
equation.SlopeGuess = k*1.0E-7; // change to adjust \Psi(r)
equation.ValueAtOriginGuess = 1.6; // change as you wish
equation.Solve();
if(equation.SolvedQ)
result += k+" Energy="+Convert.ToString(equation.Energy)+"\r\n";
}
result += "Done"; */
}
private double V(double r)
{
return -1.0/r; // change as you wish
}
}
}
/*
0 0.00923178891498278 -0.00923178891498278
0.15 0.00791650904991636 -0.00831781023169594
0.3 0.00673281572786269 -0.0074764448052233
0.45 0.00567019451575102 -0.00670271150792952
0.6 0.00471885478591681 -0.00599193768599473
0.75 0.00386968478794459 -0.00533974143286543
0.9 0.00311420930433802 -0.00474201481301265
1.05 0.00244454975813704 -0.0041949080150787
1.2 0.0018533866249551 -0.00369481435118826
1.35 0.00133392404127168 -0.00323835609723141
1.5 0.00087985647139152 -0.00282237109563548
1.65 0.000485337330418754 -0.00244390010154813
1.8 0.000144949453804346 -0.00210017482797508
1.95 -0.000146322691201697 -0.00178860665054681
2.1 -0.000393119149513885 -0.00150677593728669
2.25 -0.000599729061574707 -0.00125242197686961
2.4 -0.000770113781359224 -0.00102343346552373
2.55 -0.000907928609673265 -0.000817839525321128
2.7 -0.00101654321448539 -0.000633801229519656
2.85 -0.00109906081812967 -0.000469603603311655
3 -0.00115833621866432 -0.000323648076399516
3.15 -0.00119699271118572 -0.000194445363274949
3.3 -0.00121743797191727 -8.06087479217097E-05
3.45 -0.00122187896557455 1.9152249572314E-05
3.6 -0.00121233592671659 0.000106037842254703
3.75 -0.00119065547229602 0.000181163603318587
3.9 -0.00115852290132734 0.000245565773134229
4.05 -0.0011174737089181 0.000300206252205255
4.2 -0.00106890438807702 0.000345977313012885
4.35 -0.00101408253059049 0.000383706029407882
4.5 -0.000954156298379791 0.000414158455857084
4.65 -0.000890163271949142 0.000438043553296079
4.8 -0.000823038737224895 0.000456016889861675
4.95 -0.000753623431865679 0.000468684121604825
5.1 -0.000682670782416254 0.000476604265121277
5.25 -0.000610853666697944 0.000480292776344484
5.4 -0.000538770729027414 0.000480224445486004
5.55 -0.000466952274276543 0.000476836118023151
5.7 -0.000395865765785761 0.000470529251330035
5.85 -0.000325920951232361 0.000461672316258752
6 -0.000257474639735904 0.000450603052741099
6.15 -0.000190835150958685 0.00043763058742496
6.3 -0.000126266456811201 0.000423037421403803
6.45 -6.39920338615143E-05 0.000407081295001556
6.60000000000001 -4.19844452971669E-06 0.00038999693667522
6.75000000000001 5.29613356407768E-05 0.000371997702874793
6.90000000000001 0.000107364828530746 0.000353277115272146
7.05000000000001 0.000158917187087579 0.000334010301184416
7.20000000000001 0.000207548538211527 0.000314355342655332
7.35000000000001 0.000253211522258294 0.000294454539155664
7.50000000000001 0.000295879015320498 0.000274435589639298
7.65000000000001 0.000335542022670383 0.000254412698287996
7.80000000000001 0.000372207733504531 0.000234487608075831
7.95000000000001 0.000405897724782888 0.000214750567301364
8.10000000000001 0.000436646305278466 0.000195281232540179
8.25000000000001 0.000464498990539214 0.000176149511822901
8.40000000000001 0.000489511100779905 0.000157416351248026
8.55000000000001 0.000511746472337291 0.000139134469129455
8.70000000000001 0.000531276275309204 0.00012134904025439
8.85000000000001 0.00054817793065306 0.000104098333371754
9.00000000000001 0.000562534118968379 8.74143052999839E-05
9.15000000000001 0.000574431875219085 7.13231539342688E-05
9.30000000000001 0.000583961764679516 5.5845832048036E-05
9.45000000000001 0.000591217132474924 4.09985253991616E-05
9.60000000000001 0.000596293422305703 2.67930962187241E-05
9.75000000000001 0.000599287558808525 1.32374954062274E-05
9.90000000000001 0.00060029738915442 3.36145169116336E-07
10.05 0.000599421181887922 -1.19097072490708E-05
10.2 0.000596757175679581 -2.35016615698551E-05
10.35 0.000592403174942961 -3.44438614740704E-05
10.5 0.000586456188395914 -4.47427133911037E-05
10.65 0.000579012110605543 -5.4406627891115E-05
10.8 0.000570165440257694 -6.34457811242863E-05
10.95 0.000560009030753712 -7.18718949503594E-05
11.1 0.00054863387271847 -7.96980334436785E-05
11.25 0.00053612890963931 -8.69384176362589E-05
11.4 0.00052258087620218 -9.36082549935454E-05
11.55 0.000508074160134874 -9.97235818538807E-05
11.7 0.000492690691619153 -0.000105301120637657
11.85 0.000476509850198197 -0.000110358149705048
12 0.000459608387310141 -0.000114912382782273
12.15 0.000442060373128034 -0.000118981860982433
12.3 0.00042393715368399 -0.000122584854905626
12.45 0.000405307320550821 -0.000125739773634757
12.6 0.000386236701651859 -0.00012846508565595
12.75 0.000366788352595358 -0.000130779245535367
12.9 0.000347022566421364 -0.00013270062788477
13.05 0.000326996891063047 -0.000134247470696411
13.2 0.000306766149384969 -0.000135437820976443
13.35 0.000286382478283714 -0.000136289490841636
13.5 0.000265895358931018 -0.000136820014805328
13.65 0.000245351669380834 -0.000137046615395372
13.8 0.000224795725953426 -0.000136986171218799
13.95 0.000204269344192236 -0.000136655190312537
14.1 0.000183811889235308 -0.000136069787272268
14.25 0.000163460343394048 -0.000135245663575653
14.4 0.000143249361719147 -0.000134198091664046
14.55 0.000123211346127424 -0.000132941901982888
14.7 0.000103376502296362 -0.000131491471877198
14.85 8.3772919920915E-05 -0.00012986071937415
15 6.44266295643036E-05 -0.000128063094996616
15.15 4.5361684641031E-05 -0.000126111581785632
15.3 2.66002238890748E-05 -0.000124018689936728
15.45 8.16254297756312E-06 -0.000121796459831257
15.6 -9.93282651927262E-06 -0.000119456462843703
15.75 -2.76690623482601E-05 -0.000117009802340888
15.9 -4.50309685352718E-05 -0.000114467121844859
16.05 -6.20049074800225E-05 -0.000111838607247074
16.2 -7.85787450305427E-05 -0.000109133992794738
16.35 -9.4741767472086E-05 -0.000106362571705048
16.5 -0.000110484619288298 -0.000103533200946831
16.65 -0.000125799250782277 -0.00010065430941813
16.8 -0.000140678838617357 -9.77339104271625E-05
16.95 -0.00015511772902496 -9.47796084804157E-05
17.1 -0.000169111386038897 -9.17986090809068E-05
17.25 -0.000182656319186446 -8.87977317574432E-05
17.4 -0.000195750033677787 -8.57834179434276E-05
17.55 -0.000208390977040332 -8.27617426409338E-05
17.7 -0.000220578475518202 -7.97384268807173E-05
17.85 -0.000232312691609806 -7.67188461945746E-05
18 -0.0002435945691765 -7.37080437599573E-05
18.15 -0.000254425780428505 -7.07107414990905E-05
18.3 -0.000264808687171759 -6.77313496185978E-05
18.45 -0.000274746287251162 -6.47739799610145E-05
18.6 -0.000284242173489006 -6.18424555055838E-05
18.75 -0.000293300493933133 -5.89403215166685E-05
18.9 -0.000301925904275304 -5.60708576696363E-05
19.05 -0.000310123535779783 -5.32370867392027E-05
19.2 -0.000317898954443716 -5.04417866410604E-05
19.35 -0.000325258122794385 -4.76875006082662E-05
19.5 -0.000332207371359441 -4.49765462123464E-05
19.65 -0.000338753359137461 -4.23110271761279E-05
19.8 -0.000344903046097598 -3.96928414573461E-05
19.95 -0.000350663663756203 -3.71236913112387E-05
20.1 -0.000356042681691025 -3.46050934752425E-05
20.25 -0.000361047786212663 -3.21383864642286E-05
20.4 -0.000365686851187381 -2.97247408136036E-05
20.55 -0.000369967912252702 -2.7365167335799E-05
20.7 -0.000373899147946635 -2.50605244751954E-05
20.85 -0.000377488852503623 -2.28115279982009E-05
21 -0.000380745417543504 -2.06187574339033E-05
21.15 -0.000383677313748336 -1.84826637941853E-05
21.3 -0.000386293067665815 -1.64035780360864E-05
21.45 -0.000388601248153795 -1.438171652202E-05
21.6 -0.00039061044951017 -1.24171885059766E-05
21.75 -0.000392329272304824 -1.05100034592805E-05
21.9 -0.000393766313169571 -8.66007583520091E-06
22.05 -0.000394930149527051 -6.86723217503274E-06
22.2 -0.00039582932458329 -5.13121722243505E-06
22.35 -0.000396472339233331 -3.4516982639608E-06
22.5 -0.000396867638970419 -1.82827162050501E-06
22.65 -0.000397023602134089 -2.60467813982553E-07
22.8 -0.000396948533605301 1.25224455072945E-06
22.95 -0.000396650654216954 2.710453028829E-06
23.1 -0.000396138091233036 4.11479678043864E-06
23.25 -0.000395418873738802 5.46596327504553E-06
23.4 -0.000394500924716966 6.76468333617329E-06
23.55 -0.000393392052950477 8.01172687762177E-06
23.7 -0.000392099949869829 9.20790028366869E-06
23.85 -0.000390632184385986 1.03540423301433E-05
24 -0.000388996195830071 1.14510199734017E-05
24.1499999999999 -0.000387199291798323 1.24997264156645E-05
24.2999999999999 -0.000385248645395875 1.35010778043572E-05
24.4499999999999 -0.00038315128979228 1.44560093289411E-05
24.5999999999999 -0.00038091411610893 1.53654734501006E-05
24.7499999999999 -0.000378543872414559 1.62304374356377E-05
24.8999999999999 -0.000376047160941248 1.70518803197849E-05
25.0499999999999 -0.000373430435353888 1.78307903957395E-05
25.1999999999999 -0.0003707000005491 1.85681638952261E-05
25.3499999999999 -0.000367862012541125 1.92650028062008E-05
25.4999999999999 -0.000364922476350666 1.99223120043746E-05
25.6499999999999 -0.000361887245431387 2.05410981877395E-05
25.7999999999999 -0.000358762022515267 2.11223683742852E-05
25.9499999999999 -0.000355552360042226 2.16671282414868E-05
26.0999999999999 -0.000352263659600438 2.21763797778472E-05
26.2499999999999 -0.000348901172023019 2.26511207977864E-05
26.3999999999999 -0.000345469999180851 2.30923436144942E-05
26.5499999999999 -0.000341975095061916 2.3501033900864E-05
26.6999999999999 -0.000338421266673223 2.38781687444851E-05
26.8499999999999 -0.00033481317427062 2.42247163459272E-05
26.9999999999999 -0.000331155333521735 2.45416351246979E-05
27.1499999999999 -0.000327452117342467 2.48298730322619E-05
27.2999999999999 -0.000323707758130738 2.50903660317861E-05
27.4499999999999 -0.000319926348770489 2.53240375316682E-05
27.5999999999999 -0.0003161118431868 2.55317982572872E-05
27.7499999999999 -0.000312268060422186 2.5714545380104E-05
27.8999999999999 -0.00030839868545565 2.58731622710023E-05
28.0499999999999 -0.000304507273509379 2.60085173171078E-05
28.1999999999999 -0.000300597250621011 2.61214637777361E-05
28.3499999999999 -0.000296671913962801 2.62128397520902E-05
28.4999999999999 -0.000292734437205138 2.62834676398843E-05
28.6499999999999 -0.000288787870705452 2.63341540704398E-05
28.7999999999999 -0.000284835146848 2.6365689291532E-05
28.9499999999999 -0.000280879081619491 2.63788470041569E-05
29.0999999999999 -0.000276922374609086 2.6374384362531E-05
29.2499999999999 -0.000272967611717075 2.63530419176683E-05
29.3999999999999 -0.000269017270372531 2.63155434650359E-05
29.5499999999999 -0.000265073720256225 2.62625959846687E-05
29.6999999999999 -0.000261139228103191 2.61948895476853E-05
29.8499999999999 -0.000257215957791256 2.61130973146079E-05
29.9999999999999 -0.000253305971185052 2.60178755655066E-05
30.0000000000001 -0.000253305971187231 2.60178755671531E-05
30.1500000000001 -0.000249411234990017 2.59098639035711E-05
30.3000000000001 -0.000245533621284447 2.57896852039288E-05
30.4500000000001 -0.000241674907808052 2.56579455423842E-05
30.6000000000001 -0.000237836784896175 2.5515234617775E-05
30.7500000000001 -0.000234020856356394 2.53621258148741E-05
30.9000000000001 -0.000230228639549702 2.51991762100491E-05
31.0500000000001 -0.000226461569784905 2.50269268186584E-05
31.2000000000001 -0.000222721001101361 2.48459025600421E-05
31.3500000000001 -0.000219008211268982 2.46566127804137E-05
31.5000000000001 -0.000215324404297045 2.44595514617019E-05
31.6500000000001 -0.000211670710434184 2.42551972215499E-05
31.8000000000001 -0.000208048187580654 2.40440134477092E-05
31.9500000000001 -0.000204457826278853 2.38264487319204E-05
32.1000000000001 -0.000200900550100736 2.36029369705089E-05
32.2500000000001 -0.000197377220372188 2.33738979009155E-05
32.4000000000001 -0.000193888636454625 2.31397371308992E-05
32.5500000000001 -0.000190435536289218 2.29008462060331E-05
32.7000000000001 -0.000187018600746788 2.26576031360242E-05
32.8500000000001 -0.000183638454608591 2.24103725342164E-05
33.0000000000001 -0.000180295670130787 2.21595061006858E-05
33.1500000000001 -0.000176990767546776 2.19053426869911E-05
33.3000000000001 -0.000173724216267604 2.16482084715051E-05
33.4500000000001 -0.000170496437999317 2.13884174134728E-05
33.6000000000001 -0.000167307808474765 2.112627151738E-05
33.7500000000001 -0.00016415865954348 2.08620611443991E-05
33.9000000000001 -0.000161049279591918 2.05960650810384E-05
34.0500000000001 -0.000157979916076215 2.0328550958445E-05
34.2000000000001 -0.000154950777208439 2.0059775527762E-05
34.3500000000001 -0.000151962034005755 1.97899849922659E-05
34.5000000000001 -0.000149013820790211 1.95194150949018E-05
34.6500000000001 -0.000146106237245418 1.92482914940762E-05
34.8000000000001 -0.0001432393500997 1.89768300578254E-05
34.9500000000001 -0.000140413194714458 1.87052371383915E-05
35.1000000000001 -0.000137627775789026 1.84337097086364E-05
35.2500000000001 -0.000134883069134174 1.81624357123525E-05
35.4000000000001 -0.000132179023326877 1.78915943652155E-05
35.5500000000001 -0.000129515560649709 1.76213563290152E-05
35.7000000000001 -0.000126892578209063 1.73518839489511E-05
35.8500000000001 -0.000124309949412428 1.70833315535179E-05
36.0000000000001 -0.000121767525353484 1.68158457176088E-05
36.15 -0.000119265135472274 1.65495654051608E-05
36.3 -0.000116802588862297 1.62846222614816E-05
36.45 -0.000114379675643896 1.60211408868979E-05
36.6 -0.000111996167642473 1.57592389797293E-05
36.75 -0.000109651819430191 1.54990275857926E-05
36.9 -0.000107346369559417 1.52406113610182E-05
37.05 -0.000105079541341255 1.49840887362401E-05
37.2 -0.000102851043649937 1.47295521211815E-05
37.35 -0.000100660572035926 1.44770881570561E-05
37.5 -9.85078095104698E-05 1.42267778865683E-05
37.65 -9.63924272144812E-05 1.3978696932292E-05
37.8 -9.43140854143985E-05 1.37329157341115E-05
37.95 -9.22724342285704E-05 1.34894997119483E-05
38.1 -9.02671142198563E-05 1.32485094321299E-05
38.25 -8.82977572907444E-05 1.30100008279521E-05
38.4 -8.63639873126985E-05 1.2774025346836E-05
38.55 -8.44654206755997E-05 1.25406301129434E-05
38.7 -8.26016670941317E-05 1.23098581291084E-05
38.85 -8.07723301258501E-05 1.20817484059346E-05
39 -7.89770076970599E-05 1.18563361244427E-05
39.15 -7.72152928194969E-05 1.16336528159967E-05
39.3 -7.5486774008306E-05 1.14137264782413E-05
39.45 -7.37910357903665E-05 1.11965817348184E-05
39.6 -7.21276593243463E-05 1.09822399920824E-05
39.75 -7.04962227318317E-05 1.07707195462769E-05
39.9 -6.88963016181883E-05 1.0562035742334E-05
40.05 -6.73274695464166E-05 1.03562010979428E-05
40.2 -6.57892983412325E-05 1.01532254157532E-05
40.35 -6.4281358598483E-05 9.9531159306837E-06
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*/