|\^/| Maple 9.5 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2004 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. # # A maple program to do 1D SHO pert thy # courtesy Ted Barnes # Dept. of Physics, Univ. of Tennessee and # Theoretical Physics Group, Oak Ridge National Laboratory # # this version just generates numerical coefficients # ######################################################################## perturbation theory, scaled 1D SHO with x^4 interaction... V0 = 1/2 x^2 (m = k = hbar*w = 1), VI = g x^4 E_0(g) = sum_n=0^infty e_n g^n = 1/2 + (3/4)*g + (-21/8)*g^2 + (333/16)*g^3 + ... 1st 33 coefficients in pert thy: ____________________________ order n,coeff e_n [fraction = ratio of prime factors] = 1 0, 1/2 = ---- (2) (3) 1, 3/4 = ----- 2 (2) (3) (7) 2, -21/8 = - --------- 3 (2) 2 333 (3) (37) 3, --- = ----------- 16 4 (2) -30885 (3) (5) (29) (71) 4, ------ = - --------------------- 128 7 (2) 3 916731 (3) (19) (1787) 5, ------ = ------------------- 256 8 (2) -65518401 (3) (13) (1679959) 6, --------- = - --------------------- 1024 10 (2) 2 2723294673 (3) (11) (71) (387437) 7, ---------- = --------------------------- 2048 11 (2) -1030495099053 (3) (7) (49071195193) 8, -------------- = - ------------------------ 32768 15 (2) 2 54626982511455 (3) (5) (53) (352229) (65027) 9, -------------- = ----------------------------------- 65536 16 (2) -6417007431590595 (3) (5) (7) (379) (162623) (991567) 10, ----------------- = - ----------------------------------------- 262144 18 (2) 3 413837985580636167 (3) (29) (528528717216649) 11, ------------------ = ------------------------------ 524288 19 (2) -116344863173284543665 12, ---------------------- = 4194304 2 (3) (5) (7) (17) (139) (401) (389788090057) - --------------------------------------------------- 22 (2) 4 8855406003085477228503 (3) (11) (17) (10081409464339) (57991) 13, ---------------------- = -------------------------------------------- 8388608 23 (2) -1451836748576538293163705 14, -------------------------- = 33554432 2 (3) (5) (7) (89) (361696216746619) (143177) - -------------------------------------------------- 25 (2) 127561682802713500067360049 15, --------------------------- = 67108864 3 (3) (13) (1039) (237199633369) (1474631689) ------------------------------------------------- 26 (2) -191385927852560927887828084605 16, ------------------------------- = 2147483648 2 (3) (5) (4253020618945798397507290769) - ------------------------------------------ 31 (2) 19080610783320698048964226601511 17, -------------------------------- = 4294967296 3 (3) (151) (4680061511729383872691740643) -------------------------------------------- 32 (2) -4031194983593309788607032686292335 18, ----------------------------------- = 17179869184 (3) (5) (181) (347) (45776069111) (23692855111) (3945287) - ---------------------------------------------------------------- 34 (2) 449820604540765836160529697491458635 19, ------------------------------------ = 34359738368 2 (3) (5) (367) (709) (2317053471646255371629) (16579769) -------------------------------------------------------------- 35 (2) -211491057584560795425148309663914344715 20, ---------------------------------------- = - (3) (5) (17) (37) (43) 274877906944 38 (911) (76952363) (119435906090101) (62259611)/ (2) 26120222383762781149654970754934417034805 21, ----------------------------------------- = 549755813888 2 (3) (5) (79) (3988661915095447729386199) (3604591) (511039) ------------------------------------------------------------------ 39 (2) -6763740228794489740596394161822714805728135 22, -------------------------------------------- = 2199023255552 (3) (5) (450916015252965982706426277454847653715209) - ------------------------------------------------------- 41 (2) 916117527799746577984641800484328417887454935 23, --------------------------------------------- = 4398046511104 4 (3) (5) (324676128485699453680097461395371271581) (6967) ------------------------------------------------------------- 42 (2) -1036464696105720129803188216619901855131610583785 24, -------------------------------------------------- = 70368744177664 (3) (5) (11) (94525167539395502039191) (66454303994801655048019) - --------------------------------------------------------------------- 46 (2) 152773774949844438983482018830957022324392611587683 25, --------------------------------------------------- = 140737488355328 2 (3) (101) (601) (1035182058230864749913392363546581014009) (270143) ------------------------------------------------------------------------- 47 (2) -46864661934282542604967271035084212028364938136115903 26, ------------------------------------------------------ = - (3) (29) 562949953421312 49 (265026187827000909965444671346253931) (48862472167) (41597)/ (2) 7468424771414634117845409123534119931849505977965315619 2 27, ------------------------------------------------------- = (3) (11) (23) 1125899906842624 / (29) (1896082192216006135151) (11517677444117951943274567) (5179) / / 50 (2) -4939479898777642568776881638048610516053578367250019222857 28, ----------------------------------------------------------- = 9007199254740992 (3) (1688444998376094110352771739150865293867) (975153647987411657) - ---------------------------------------------------------------------- 53 (2) 846284774074565106837237848622053215062153108475654677813615 5 29, ------------------------------------------------------------ = (3) (5) 18014398509481984 / (133531303649053323442382323594759098495554169499) (149381) (34919) / / 54 (2) -300121824583301012159970897013428849261973957431788548963467657 4 30, ---------------------------------------------------------------- = - (3) 72057594037927936 (7) (17) (127) (6604366819636273106298117793113962773) (4556999) / 56 (18329) (1753) (253531) / (2) / 55013796260436012961915328581386011752918767976598738126819263089 3 31, ----------------------------------------------------------------- = (3) 144115188075855872 (2075520431916843488342158483) (26330474619805711) (464743249307) / 57 (30469) (2633) / (2) / -333240020344369737849675013849465176026142994492806680094689746926621 32, ---------------------------------------------------------------------- = - 9223372036854775808 3 (3) (191) (9841452628781855821) (6898471867166726947) (84979439203) / 63 (335070855799) (33427) / (2) / 65076055174022071568381890075793502303462805706717017711390547642799543 33, ----------------------------------------------------------------------- = 18446744073709551616 3 (3) (13) (77461448531464675621) (1119610854791372189) / 64 (6315724918975079) (42899639) (7890137) / (2) / ____________________________ Physicists just wanna have fun.