Penyelesaian Potensial Gendenshtein IV dengan PD
Hypergeometry
Oleh :
ISMAIL (S911408001)
PROGRAM STUDI ILMU FISIKA
PROGRAM PASCASARJANA
UNIVERSITAS SEBELAS MARET SURAKARTA
2015
Penyelesaian Potensial Gendenshtein IV dengan PD
Hypergeometry
Persamaan potensial Gendenshtein IV dinyatakan dengan :
(1)
Persamaan Schrodinger untuk potensial Gendenshtein IV dapat
dinyatakan sebagai :
(2)
dimisalkan
Dengan substitusi persamaan (3) dan (4) ke persamaan (2)
diperoleh hasil :
dengan mengalikan semua suku dengan diperoleh hasil :
Dengan memisalkan diperoleh hasil :
Persamaan (I) dapat diubah menjadi
(Catatan Penting)
(Catatan Penting)
Sehingga persamaan (6) menjadi
Persamaan (7) merupakan persamaan differensial orde dua homogeny
yang mempunyai titik regular singular di titik z = 0 atau z = 1
Untuk titik z = 0
Suku dan diabaikan terhadap suku , sehingga persamaan (7)
menjadi :
Sedangkan untuk z = 1
Suku dan diabaikan terhadap suku sehingga persamaan (7) menjadi
:
Fungsi Baru
Dari persamaan fungsi baru di atas, persamaan (7) menjadi :
Persamaan (a)
Persamaan (b)
Persamaan (c)
Persamaan (d)
Sehingga persamaannya menjadi :
Pengubahan parameter
Untuk
Untuk
Disubtitusikan kembali ke persamaan diperoleh :
Persamaan di atas identik dengan PD orde dua Fungsi
Hypergeometry
dimana
Penentuan nilai dan
Menentukan spectrum energy
dengan memilih a = - n
Menentukan fungsi gelombang tingkat dasar
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