งก, นกำเน, บทความน, ไม, การอ, างอ, งจากแหล, งท, มาใดกร, ณาช, วยปร, บปร, งบทความน, โดยเพ, มการอ, างอ, งแหล, งท, มาท, าเช, อถ, เน, อความท, ไม, แหล, งท, มาอาจถ, กค, ดค, านหร, อลบออก, เร, ยนร, าจะนำสารแม, แบบน, ออกได, อย, างไรและเม, อไร, ในทางฟ, กส, generating, fu. bthkhwamniimmikarxangxingcakaehlngthimaidkrunachwyprbprungbthkhwamni odyephimkarxangxingaehlngthimathinaechuxthux enuxkhwamthiimmiaehlngthimaxacthukkhdkhanhruxlbxxk eriynruwacanasaraemaebbnixxkidxyangiraelaemuxir inthangfisiks fngkchnkaenid Generating function approach khuxkarichxnuphnthyxysrangsmkarechingxnuphnththixthibaythungphlsastrkhxngrabb twxyangthwip echn fngkchnaebngswn Partition function khxngklsastrsthiti hruxhamilotheniyn Hamiltonian hruxfngkchnthithahnathiaesdngkhwamsmphnthrahwang 2 estkhxngtwaeprkhaonnikhl Canonical variable sahrbkaraeplngaebbbyyti Canonical transformation sahrbkaraeplngaebbbyyti ephuxtrwcsxbkhwamthuktxngkhxngkaraeplngfngkchnrahwang q p H aela Q P K sungthngsxngestcatxngepniptamhlkkarhamiltn Hamilton s principle odysamarthekhiynsmkarlakrancid khux L q p p q H q p t displaystyle mathcal L qp mathbf p cdot dot mathbf q H mathbf q mathbf p t aela L Q P P Q K Q P t displaystyle mathcal L QP mathbf P cdot dot mathbf Q K mathbf Q mathbf P t tamladb odythikaraeplngelxcxngk Legendre transform catxngmikhakhngtw nnkhux d t 1 t 2 p q H q p t d t 0 d t 1 t 2 P Q K Q P t d t 0 displaystyle begin aligned delta int t 1 t 2 left mathbf p cdot dot mathbf q H mathbf q mathbf p t right dt amp 0 delta int t 1 t 2 left mathbf P cdot dot mathbf Q K mathbf Q mathbf P t right dt amp 0 end aligned thngsxngsmkarcaidkhwamsmphnth dngni l p q H q p t P Q K Q P t d G d t displaystyle lambda left mathbf p cdot dot mathbf q H mathbf q mathbf p t right mathbf P cdot dot mathbf Q K mathbf Q mathbf P t frac dG dt odythi G caepnfngkchnkaenid Generating function khunkbphikdaelaomemntmthnginrabbeka q hrux p aelarabbihm rabbeka Q hrux P aela l caepntwprbkhnadkhxngkaraeplng Scale transformation sahrbkaraeplngaebbbyyticaih l 1 displaystyle lambda 1 sahrbkaraeplngaebbbyyti camifngkchnkaenidthnghmd 4 rupaebb dngni enuxha 1 rupaebbthi 1 khxngfngkchnkaenid 2 rupaebbthi 2 khxngfngkchnkaenid 3 rupaebbthi 3 khxngfngkchnkaenid 4 rupaebbthi 4 khxngfngkchnkaenidrupaebbthi 1 khxngfngkchnkaenid aekikhG 1 displaystyle G 1 khunkbphikdkhxngthngrabbekaaelaihm G G 1 q Q t displaystyle G equiv G 1 mathbf q mathbf Q t samarthekhiynsmkarid dngni p q H q p t P Q K Q P t G 1 t G 1 q q G 1 Q Q displaystyle mathbf p cdot dot mathbf q H mathbf q mathbf p t mathbf P cdot dot mathbf Q K mathbf Q mathbf P t frac partial G 1 partial t frac partial G 1 partial mathbf q cdot dot mathbf q frac partial G 1 partial mathbf Q cdot dot mathbf Q enuxngcakphikdrabbekaaelaihmepnxisratxkn dngnnsmkarkhangtncaepncringktxemux p G 1 q P G 1 Q K H G 1 t displaystyle begin aligned mathbf p amp frac partial G 1 partial mathbf q mathbf P amp frac partial G 1 partial mathbf Q K amp H frac partial G 1 partial t end aligned rupaebbthi 2 khxngfngkchnkaenid aekikhG 2 displaystyle G 2 khunkbphikdkhxngrabbekakbomemntmkhxngrabbihm G Q P G 2 q P t displaystyle G equiv mathbf Q cdot mathbf P G 2 mathbf q mathbf P t samarthekhiynsmkarid dngni p q H q p t Q P K Q P t G 2 t G 2 q q G 2 P P displaystyle mathbf p cdot dot mathbf q H mathbf q mathbf p t mathbf Q cdot dot mathbf P K mathbf Q mathbf P t frac partial G 2 partial t frac partial G 2 partial mathbf q cdot dot mathbf q frac partial G 2 partial mathbf P cdot dot mathbf P enuxngcakphikdkhxngrabbekaaelaomemntmkhxngrabbihmepnxisratxkn dngnnsmkarkhangtncaepncringktxemux p G 2 q Q G 2 P K H G 2 t displaystyle begin aligned mathbf p amp frac partial G 2 partial mathbf q mathbf Q amp frac partial G 2 partial mathbf P K amp H frac partial G 2 partial t end aligned rupaebbthi 3 khxngfngkchnkaenid aekikhG 3 displaystyle G 3 khunkbomemntmkhxngrabbekakbphikdkhxngrabbihm G q p G 3 p Q t displaystyle G equiv mathbf q cdot mathbf p G 3 mathbf p mathbf Q t samarthekhiynsmkarid dngni q p H q p t P Q K Q P t G 3 t G 3 p p G 3 Q Q displaystyle mathbf q cdot dot mathbf p H mathbf q mathbf p t mathbf P cdot dot mathbf Q K mathbf Q mathbf P t frac partial G 3 partial t frac partial G 3 partial mathbf p cdot dot mathbf p frac partial G 3 partial mathbf Q cdot dot mathbf Q enuxngcakomemntmkhxngrabbekaaelaphikdkhxngrabbihmepnxisratxkn dngnnsmkarkhangtncaepncringktxemux q G 3 p P G 3 Q K H G 3 t displaystyle begin aligned mathbf q amp frac partial G 3 partial mathbf p mathbf P amp frac partial G 3 partial mathbf Q K amp H frac partial G 3 partial t end aligned rupaebbthi 4 khxngfngkchnkaenid aekikhG 4 displaystyle G 4 khunkbomemntmkhxngthngrabbekaaelaihm G q p Q P G 4 p P t displaystyle G equiv mathbf q cdot mathbf p mathbf Q cdot mathbf P G 4 mathbf p mathbf P t samarthekhiynsmkarid dngni q p H q p t Q P K Q P t G 4 t G 4 p p G 4 P P displaystyle mathbf q cdot dot mathbf p H mathbf q mathbf p t mathbf Q cdot dot mathbf P K mathbf Q mathbf P t frac partial G 4 partial t frac partial G 4 partial mathbf p cdot dot mathbf p frac partial G 4 partial mathbf P cdot dot mathbf P enuxngcakomemntmkhxngrabbekaaelaihmepnxisratxkn dngnnsmkarkhangtncaepncringktxemux q G 4 p Q G 4 P K H G 4 t displaystyle begin aligned mathbf q amp frac partial G 4 partial mathbf p mathbf Q amp frac partial G 4 partial mathbf P K amp H frac partial G 4 partial t end aligned ekhathungcak https th wikipedia org w index php title fngkchnkaenid amp oldid 8023467, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,