using System;
using Science.Mathematics;
using L = Science.Physics.QuantumMechanics;
namespace ScienceTest.PhysicsTest.QuantumMechanicsTest
{
///
/// We solve the differential equation : R(r) = r^|m| \Psi(r)
/// -0.5{\Psi''(r) + (2m+1)/r\Psi'(r)} + V(r)\Psi(r) = E\Psi(r)
///
public class SchroedingerEq2DTest
{
public SchroedingerEq2DTest()
{
}
private string result;
public string Result
{
get{return result;}
}
public void Compute()
{
L.SchroedingerEquation2D equation = new L.SchroedingerEquation2D();
Function.ToLastType func = new Function.ToLastType(V);
equation.PotentialEnergy = func;
equation.RadialBoundary = 12.0; // radius should be large enough for wavefunction to be 0
equation.EnergyGuess = 4.87; // change as you wish
equation.SlopeGuess = -5.0E-15; // change to adjust \Psi(r)
equation.ValueAtOriginGuess = 12.0; // 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 += "Energy="+Convert.ToString(equation.Energy)+"\r\n";
}
private double V(double r)
{
return 0.5*r*r; // change as you wish
}
}
}
/*
0 9.18292019469931 0
0.03 9.09634686060015 -5.75788598625799
0.06 8.83907958078858 -11.3526903542612
0.09 8.41839880704013 -16.6264979550799
0.12 7.84618218731391 -21.4315528409577
0.15 7.13852896467453 -25.6349096140471
0.18 6.31525192164329 -29.1225877294761
0.21 5.39925390505727 -31.8030905038433
0.24 4.41580979149402 -33.6101728046878
0.27 3.39177784974716 -34.5047676240595
0.3 2.35476671771382 -34.4760110164362
0.33 1.33228556133219 -33.5413361545907
0.36 0.350905379090139 -31.745639398053
0.39 -0.564541151165154 -29.1595531281496
0.42 -1.39169539060002 -25.8768905441659
0.45 -2.11132051293138 -22.0113555615879
0.48 -2.70784099425934 -17.6926354247888
0.51 -3.16975732268997 -13.0620137986289
0.54 -3.48992380462895 -8.26765725174007
0.57 -3.66568209097213 -3.4597376946351
0.6 -3.69884799588664 1.21444280388099
0.63 -3.59555415805102 5.6151604073441
0.66 -3.36595592452236 9.61465443750302
0.69 -3.02381235340509 13.1010453001212
0.72 -2.58595827893784 15.98165987299
0.75 -2.07168682579811 18.1856609754191
0.78 -1.50206448589048 19.6659030113909
0.810000000000001 -0.899202795223482 20.3999637151916
0.840000000000001 -0.285511714999499 20.3903311041416
0.870000000000001 0.317039994539828 19.6637542000501
0.900000000000001 0.887632809380531 18.2697947667063
0.930000000000001 1.40724981459319 16.2786442172901
0.960000000000001 1.85925463875214 13.7782940453972
0.990000000000001 2.22987614438992 10.8711688123847
1.02 2.50858559841299 7.67034720915453
1.05 2.68835600094723 4.2955084923727
1.08 2.7657974841445 0.868748343450317
1.11 2.74116705048164 -2.48959022986231
1.14 2.61825524791895 -5.6649288877149
1.17 2.40415652608815 -8.55217524447383
1.2 2.10893384207605 -11.0590327985671
1.23 1.74519145942435 -13.1087957543023
1.26 1.32757270141433 -14.642545137731
1.29 0.872201593399245 -15.6206852318996
1.32 0.396088797605961 -16.0237835914622
1.35 -0.0834770275682468 -15.8527028472089
1.38 -0.549531331149079 -15.1280372770106
1.41 -0.98600887203424 -13.8888908293828
1.44 -1.37827309014211 -12.1910551269384
1.47 -1.71358276789442 -10.1046652248679
1.5 -1.98148168626488 -7.71142694056328
1.53 -2.17409998907646 -5.10152192260384
1.56 -2.28635928953215 -2.37030495264847
1.59 -2.31607706011851 0.385087912339688
1.62 -2.26396941385698 3.06910187675839
1.65 -2.1335548856611 5.59098238550273
1.68 -1.930965137397 7.86774440552106
1.71 -1.66467152920513 9.82679742250159
1.74 -1.34513912639196 11.4081460683113
1.77 -0.984421865945334 12.5661031520231
1.8 -0.595714228664194 13.2704704173684
1.83 -0.192875811666915 13.5071618918009
1.86 0.210054347426898 13.2782645133524
1.89 0.599336976810014 12.6015501203333
1.92 0.961989290243521 11.5094712027302
1.95 1.28620442944668 10.0476894400347
1.98 1.56172053139703 8.27320046490791
2.01 1.78012840968339 6.25213006779944
2.04 1.93510923545827 4.0572858741841
2.07 2.02259621734845 1.76555417787272
2.1 2.04085701432253 -0.544765985943839
2.13 1.99049637362904 -2.79660026638189
2.16 1.87438117265774 -4.91662056278865
2.19 1.69749256993965 -6.83757011295521
2.22 1.46671225614706 -8.50032073061648
2.25 1.19055177170345 -9.85560216066565
2.28 0.878835467436132 -10.8653564933433
2.31 0.542348887113488 -11.5036846793707
2.34 0.192465119750813 -11.7573668931222
2.37 -0.159238005125597 -11.6259532774498
2.4 -0.501357119122009 -11.1214359658738
2.43 -0.823026685111123 -10.2675267454646
2.46 -1.11425522437324 -9.0985768759593
2.49 -1.36622434647236 -7.65818605956288
2.52 -1.57154207044623 -5.9975560749701
2.55 -1.72444369215725 -4.17365094179679
2.58 -1.82093537539629 -2.2472295425404
2.61 -1.85887765387589 -0.280818357627027
2.64 -1.83800805806862 1.66330859607271
2.67 -1.75990405765303 3.52507827589039
2.7 -1.62788937439699 5.24843596336854
2.73 -1.44688841529471 6.78297833323379
2.76 -1.22323505338742 8.08535707182052
2.79 -0.964443204888027 9.12041696190236
2.82 -0.678947587152646 9.86204222392258
2.85 -0.37582367444663 10.2936952046233
2.88 -0.0644961898677124 10.4086418770207
2.91 0.245554514757491 10.2098687191696
2.94 0.54507912082259 9.70970505730045
2.97 0.825330531375268 8.92917361049217
3 1.07831186901366 7.89709952017899
3.02999999999999 1.29699457190542 6.64901439789112
3.05999999999999 1.47550104854482 5.22589674000268
3.08999999999999 1.60924764562258 3.67279335420748
3.11999999999999 1.69504505278467 2.03736818792533
3.14999999999999 1.73115466675835 0.368425164879404
3.17999999999999 1.71730082037888 -1.28554960785306
3.20999999999999 1.65464010724789 -2.87778349136996
3.23999999999999 1.54569026183586 -4.36451184236576
3.26999999999999 1.39422215454269 -5.70613723879721
3.29999999999999 1.20511940405155 -6.86822484457694
3.32999999999999 0.984210874082484 -7.82231156816521
3.35999999999999 0.73808189388245 -8.54651325474871
3.38999999999999 0.473870413708758 -9.02592088355251
3.41999999999999 0.199054477048111 -9.25278340462495
3.44999999999999 -0.078762634529434 -9.22648124207545
3.47999999999999 -0.35206343923201 -8.95330043170635
3.50999999999999 -0.613617711702227 -8.44602269398577
3.53999999999999 -0.856669124508744 -7.72335133976338
3.56999999999999 -1.07510249604769 -6.80919666826926
3.59999999999999 -1.26358782143938 -5.7318473787279
3.62999999999999 -1.41769808991869 -4.523056443822
3.65999999999999 -1.53399876281727 -3.21707088200279
3.68999999999999 -1.61010767271307 -1.84963494179831
3.71999999999999 -1.64472498001688 -0.45699542657119
3.74999999999999 -1.63763366341724 0.925063682422336
3.77999999999999 -1.58967180299834 2.26213240939269
3.80999999999999 -1.5026786203344 3.52200972420697
3.83999999999999 -1.37941685270948 4.6754434992141
3.86999999999999 -1.22347454680294 5.69676038988263
3.89999999999999 -1.03914975244232 6.56437440470223
3.92999999999999 -0.831321874995623 7.26116687320304
3.95999999999999 -0.605313604810621 7.77473443071397
3.98999999999999 -0.366747386595424 8.09750540373262
4.01999999999999 -0.121400326564779 8.22672850243946
4.04999999999999 0.124938730878441 8.16434092218813
4.07999999999999 0.366606481249587 7.916725754643
4.10999999999999 0.598193650635097 7.49437095907199
4.13999999999999 0.814661953393036 6.91144400914352
4.16999999999999 1.01144721655152 6.18529769120399
4.19999999999999 1.18454684885923 5.33592338333166
4.22999999999999 1.33059032894759 4.38536850150322
4.25999999999999 1.44689188703004 3.35713468574945
4.28999999999999 1.53148504460138 2.27557275067885
4.31999999999999 1.58313914416533 1.16528948844713
4.34999999999999 1.60135843536979 0.0505801410020097
4.37999999999999 1.58636467584244 -1.04510118825901
4.40999999999999 1.53906454717775 -2.09962267319816
4.43999999999999 1.46100347348232 -3.09259885363541
4.46999999999999 1.3543076580841 -4.00575107059538
4.49999999999999 1.22161632174563 -4.82319966866204
4.52999999999999 1.06600623305389 -5.53168538080053
4.55999999999999 0.890910670198328 -6.12071922597251
4.58999999999999 0.700034946240073 -6.58266204023519
4.61999999999999 0.497270571470274 -6.91273639054852
4.64999999999999 0.286610021922128 -7.10897505707359
4.67999999999999 0.072063938631415 -7.17211149211363
4.70999999999999 -0.142417595484982 -7.10541865741222
4.73999999999999 -0.353018258274916 -6.91450339909691
4.77 -0.556121950854147 -6.60706404084864
4.8 -0.748371535635963 -6.19261916702365
4.83 -0.926719106325886 -5.68221564020629
4.86 -1.08846728622034 -5.08812376830184
4.89 -1.23130128432848 -4.42352722561925
4.92 -1.35331166032747 -3.70221486326609
4.95 -1.45300795467978 -2.93828094246546
4.98 -1.52932352587287 -2.14583961641532
5.01 -1.58161209985202 -1.33875869935612
5.04 -1.60963667539807 -0.530416921611564
5.07 -1.61355154218609 0.266511997412896
5.1 -1.59387825515267 1.04024599656973
5.13 -1.5514764697988 1.78005043096642
5.16 -1.48751057901096 2.47636214549249
5.19 -1.40341310427202 3.12088182957708
5.22 -1.30084578457825 3.70663531245919
5.25 -1.1816592771523 4.228005074301
5.28 -1.04785233760354 4.68073377933738
5.31 -0.901531286141344 5.06190207854404
5.34 -0.744870493580019 5.36988327894317
5.37 -0.580074538801024 5.60427773542365
5.4 -0.409342600960601 5.76582999132999
5.43 -0.234835557357677 5.85633178105075
5.46 -0.0586461642331255 5.87851401743017
5.49 0.117227395248895 5.83593082653807
5.52 0.290904401720533 5.73283857087183
5.55 0.46064082070085 5.57407262794189
5.58 0.624844825546798 5.36492447442283
5.61 0.782088666596135 5.11102137536444
5.64 0.931116995718924 4.81821070317275
5.67 1.07085181194571 4.49245062042965
5.7 1.20039424135471 4.13970856290135
5.73 1.31902340305588 3.76586866119098
5.76 1.42619264285365 3.37664894865965
5.79 1.52152343739196 2.97752892482975
5.82 1.60479728469569 2.57368778250187
5.85 1.67594590262029 2.1699533671726
5.88 1.73504005548363 1.77076172189061
5.91 1.78227732183236 1.38012688146561
5.94 1.817969103743 1.00162041836201
5.97000000000001 1.84252716101873 0.638360108747949
6 1.85644993306496 0.293006981129217
6 1.85644993306497 0.293006981129229
6.02999999999999 1.8603088878293 -0.0322300693664442
6.06 1.85473511181731 -0.335582971869759
6.09 1.84040632856122 -0.615707376918957
6.12 1.81803450570196 -0.87166066974148
6.15 1.78835418366155 -1.10287599911784
6.18 1.75211163226274 -1.30913319417759
6.21 1.71005491608092 -1.49052740029614
6.24 1.6629249251225 -1.64743621242065
6.27 1.61144740500782 -1.78048602241474
6.3 1.5563260003304 -1.89051822844491
6.33 1.49823630652124 -1.97855588156356
6.36 1.43782090941514 -2.04577126937187
6.39 1.37568537785532 -2.09345486084118
6.42 1.31239516307655 -2.12298596170313
6.45 1.2484733492156 -2.13580535764561
6.48 1.18439919201721 -2.13339015400449
6.51 1.1206073775167 -2.11723095673105
6.54 1.05748792902915 -2.0888114807414
6.57 0.995386689000079 -2.04959061891777
6.6 0.934606301991928 -2.00098695826065
6.63 0.87540762610738 -1.94436568919806
6.66 0.818011502302461 -1.88102781975516
6.69 0.762600814126311 -1.8122015781092
6.72 0.709322774271294 -1.73903586467438
6.75 0.658291378746727 -1.66259559800347
6.78 0.609589974351353 -1.58385878699544
6.81 0.563273890262654 -1.50371515474237
6.84 0.519373089856842 -1.4229661363132
6.87 0.477894804203289 -1.34232607336849
6.9 0.438826113942336 -1.26242443220187
6.93 0.402136451368993 -1.18380887811683
6.96 0.367779999435348 -1.10694904747667
6.99 0.33569796899728 -1.03224086885852
7.02 0.305820739920424 -0.960011296064421
7.05 0.278069855597195 -0.890523327907542
7.08 0.252359863989938 -0.82398120234424
7.11 0.228600001495896 -0.760535665356129
7.14 0.206695718725953 -0.700289227730383
7.17 0.186550049706768 -0.643301335313913
7.2 0.168064828069002 -0.589593390246374
7.23 0.151141755487539 -0.539153571950364
7.26000000000001 0.13568332901699 -0.491941417171147
7.29000000000001 0.121593635039621 -0.447892128025021
7.32000000000001 0.108779018340416 -0.406920585785668
7.35000000000001 0.0971486353717872 -0.368925055984474
7.38000000000001 0.0866149010972635 -0.33379057732034
7.41000000000001 0.0770938389363274 -0.301392032881811
7.44000000000001 0.0685053432982741 -0.271596907307808
7.47000000000001 0.060773364017973 -0.244267737798434
7.50000000000001 0.0538260217147517 -0.219264270384984
7.53000000000001 0.047595662709982 -0.196445335637716
7.56000000000001 0.0420188616804396 -0.17567046009601
7.59000000000001 0.0370363797119392 -0.156801231214663
7.62000000000001 0.0325930848680522 -0.139702434599459
7.65000000000001 0.0286378418165885 -0.124242982821607
7.68000000000001 0.0251233764752398 -0.11029665521934
7.71000000000001 0.0220061210579696 -0.0977426678773448
7.74000000000001 0.0192460443348621 -0.086466092479236
7.77000000000001 0.0168064713675502 -0.0763581420084303
7.80000000000001 0.0146538964561652 -0.067316340378358
7.83000000000001 0.0127577925363729 -0.0592445920475241
7.86000000000001 0.0110904197999863 -0.0520531665587353
7.89000000000001 0.00962663588199861 -0.0456586117688722
7.92000000000001 0.00834370956172917 -0.0399836083353861
7.95000000000001 0.00722113956702815 -0.0349567768249121
7.98000000000001 0.00624047974710313 -0.0305124476264103
8.01000000000001 0.00538517159155157 -0.0265904027064417
8.04000000000001 0.00464038481850424 -0.0231355971478129
8.07000000000001 0.0039928665322889 -0.0200978673773692
8.10000000000001 0.00343079925855487 -0.0174316320204463
8.13000000000001 0.00294366800028857 -0.0150955904234994
8.16000000000001 0.00252213631939802 -0.01305242306534
8.19000000000001 0.0021579313333193 -0.0112684973322553
8.22000000000001 0.00184373742207545 -0.00971358146214829
8.25000000000001 0.00157309836617473 -0.00836056886574575
8.28000000000001 0.00134032757760222 -0.00718521450640549
8.31000000000001 0.0011404260427409 -0.00616588455980964
8.34000000000001 0.000969007565560058 -0.0052833201773023
8.37000000000001 0.000822230879917398 -0.00452041583677944
8.40000000000001 0.000696738189735866 -0.00386201247838851
8.43000000000001 0.000589599693590406 -0.00329470538388998
8.46000000000001 0.000498263654497722 -0.00280666656353208
8.49000000000001 0.000420511585224541 -0.00238748125808268
8.52000000000001 0.000354418133110231 -0.00202799804162689
8.55000000000001 0.00029831526528108 -0.00172019191863955
8.58000000000001 0.000250760374381615 -0.00145703974265518
8.61000000000001 0.000210507945841798 -0.00123240723985562
8.64000000000001 0.000176484449618572 -0.00104094689564661
8.67000000000001 0.000147766141787381 -0.000878005952723627
8.70000000000001 0.000123559483884399 -0.000739543772444083
8.73000000000001 0.000103183910163618 -0.000622057825043223
8.76000000000001 8.60566946538272E-05 -0.000522517596142896
8.79000000000001 7.16796908694242E-05 -0.000438305725250763
8.82000000000001 5.96277370730494E-05 -0.000367165724813128
8.85000000000001 4.95385389969391E-05 -0.000307155664507829
8.88000000000001 4.1103859820066E-05 -0.000256607243611712
8.91000000000001 3.40618639271283E-05 -0.000214089713476385
8.94 2.81904765225136E-05 -0.000178378151560454
8.97000000000001 2.33016355428056E-05 -0.000148425627442882
9.00000000000001 1.92363255251971E-05 -0.000123338839246273
9.03 1.58602951833319E-05 -0.000102356835535
9.06 1.30603714610338E-05 -8.48324727112515E-05
9.09 1.07412928327249E-05 -7.02162910043027E-05
9.12 8.82299365567419E-06 -5.80425231946703E-05
9.15 7.23827951542338E-06 -4.79169791571743E-05
9.18 5.93084080576223E-06 -3.95065761210918E-05
9.21 4.85355831189075E-06 -3.25303092444434E-05
9.24 3.9670603829729E-06 -2.67514797315832E-05
9.27 3.23849644895555E-06 -2.19710183593612E-05
9.3 2.64049621499226E-06 -1.80217610080213E-05
9.33 2.15028791059843E-06 -1.47635497214432E-05
9.36 1.74895253229974E-06 -1.20790480597008E-05
9.39 1.42079414688698E-06 -9.87017317089022E-06
9.42 1.15280906295575E-06 -8.05505921735439E-06
9.45 9.34239073128425E-07 -6.56547766117227E-06
9.48 7.56196056590268E-07 -5.34464955951625E-06
9.51 6.11347046420442E-07 -4.34539355306767E-06
9.54 4.93650440443363E-07 -3.52856075541691E-06
9.57 3.98135396681261E-07 -2.86171436767337E-06
9.6 3.20717630831708E-07 -2.31801764366735E-06
9.63 2.58045846616331E-07 -1.87529890327535E-06
9.66 2.07373901060859E-07 -1.51526671458875E-06
9.69 1.66454554068886E-07 -1.22285221253403E-06
9.72 1.3345129138047E-07 -9.85658859157612E-07
9.75 1.06865256465327E-07 -7.9350283905205E-07
9.78 8.54747927683253E-08 -6.38029777003045E-07
9.81 6.82854940947059E-08 -5.12395612752722E-07
9.84 5.4488997478266E-08 -4.11001313356526E-07
9.87 4.34290381181136E-08 -3.29272686130808E-07
9.9 3.4573527236854E-08 -2.63477908971985E-07
9.93 2.7491617415902E-08 -2.10576550557388E-07
9.96 2.18348916227609E-08 -1.6809483742714E-07
9.99 1.7321956539987E-08 -1.34022761856196E-07
10.02 1.37258420450363E-08 -1.06729334408977E-07
10.05 1.08637103051659E-08 -8.48928861633201E-08
10.08 8.5884629684342E-09 -6.74438334904882E-08
10.11 6.78190593726617E-09 -5.35177465945617E-08
10.14 5.34919041089817E-09 -4.24169235173486E-08
10.17 4.21429815669848E-09 -3.35789741733574E-08
10.2 3.31637991166635E-09 -2.65511729269431E-08
10.23 2.60678977689054E-09 -2.09695507704724E-08
10.26 2.04668659230177E-09 -1.65418757317709E-08
10.29 1.6050965313656E-09 -1.30338182188043E-08
10.32 1.25735034843062E-09 -1.02577212795155E-08
10.35 9.83824527924793E-10 -8.06349818819483E-09
10.38 7.68928597830143E-10 -6.33126474240589E-09
10.41 6.00291559527677E-10 -4.96538402001206E-09
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10.5 2.83691391401952E-10 -2.37860369847756E-09
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10.56 1.71154927465679E-10 -1.44787014578491E-09
10.59 1.32717913810286E-10 -1.12767663583282E-09
10.62 1.0279761504518E-10 -8.7728674975104E-10
10.65 7.95335979267343E-11 -6.81712833719258E-10
10.68 6.14657313570292E-11 -5.29133385470141E-10
10.71 4.74494341137606E-11 -4.10235766283179E-10
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10.8 2.16833047675165E-11 -1.89878192647303E-10
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11.01 3.35521302465806E-12 -3.02452068762302E-11
11.04 2.55879012674583E-12 -2.31595610891041E-11
11.07 1.94927376330486E-12 -1.77140683051162E-11
11.1 1.48332128989905E-12 -1.35338469883635E-11
11.13 1.12751532790986E-12 -1.0328562665906E-11
11.16 8.56120924883001E-13 -7.87362832809522E-12
11.19 6.49342448508129E-13 -5.99552246659132E-12
11.22 4.91970522945879E-13 -4.56033730160088E-12
11.25 3.72333010906663E-13 -3.46485772862739E-12
11.28 2.81482708553927E-13 -2.62962041625683E-12
11.31 2.12569101386676E-13 -1.99352026848092E-12
11.34 1.60353062361935E-13 -1.50962450393333E-12
11.37 1.20832421439517E-13 -1.141927995133E-12
11.4 9.0953424697651E-14 -8.62841324202761E-13
11.43 6.83886479428988E-14 -6.51248491239131E-13
11.46 5.1366264126189E-14 -4.91006940167296E-13
11.49 3.85389464408156E-14 -3.69790597192258E-13
11.52 2.88833252875156E-14 -2.78198578000865E-13
11.55 2.16229693059235E-14 -2.09069402795962E-13
11.58 1.61694558053813E-14 -1.56953984750837E-13
11.61 1.20773342923727E-14 -1.17711135017996E-13
11.64 9.00974691431636E-15 -8.81974930693721E-14
11.67 6.71221305160465E-15 -6.60301470049563E-14
11.7 4.99266011957095E-15 -4.94051496332913E-14
11.73 3.70622648304037E-15 -3.69589731264147E-14
11.76 2.743704562555E-15 -2.76629217409548E-14
11.79 2.02275554332337E-15 -2.07428296703036E-14
11.82 1.48122932234025E-15 -1.56181595342612E-14
11.85 1.07207818194367E-15 -1.18560038763136E-14
11.88 7.59470768523353E-16 -9.13656970732273E-15
11.91 5.15802421493294E-16 -7.22756738628498E-15
11.94 3.1936493548638E-16 -5.96558783202096E-15
11.97 1.52488078620792E-16 -5.24308277721992E-15
12 0 -5E-15
Energy=21.0000000000019
*/