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Program Studi Ilmu Fisika, Program Pascasarjana Universitas Sebelas Maret Surakarta

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Analisis Fungsi Gelombang dan Spektrum Energi Potensial Rosen Morse Menggunakan Metode Hipergeometri Suparmi Suparmi; Nurhayati Nurhayati; Viska Inda Variani; Cari Cari
Jurnal Matematika & Sains Vol 17, No 2 (2012)
Publisher : Institut Teknologi Bandung

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Abstract

Perilaku partikel atomik dapat dipahami dengan jelas bila energi dan fungsi gelombang dari partikel tersebut diketahui. Spektrum energi dan fungsi gelombang untuk partikel yang dipengaruhi oleh potensial Rosen Morse dianalisis menggunakan metode hipergeometri. Persamaan Schrödinger untuk potensial Rosen Morse diubah menjadi persamaan diferensial orde dua fungsi hipergeometri dengan substitusi variabel dan parameter secara tepat. Spektrum energi diperoleh secara eksak dan fungsi gelombang dinyatakan dalam bentuk polinomial hipergeometri. Grafik potensial efektif dengan spektrum energi, fungsi gelombang tingkat dasar, tingkat pertama dan kedua serta rapat probabilitasnya divisualisasikan dengan menggunakan bahasa pemograman Delphi 7.0. Kata kunci: Hipergeometri, Potensial Rosen Morse, Spektrum energi, Fungsi gelombang.   Analysis of Rosen More’s Wave Function and Potential Energy Spectrum using Hypergeometric Method Abstract Behavior of atomic particles can be clearly understood if the energy and wave functions of the particle are known. Energy spectrum and wave functions for particles governed by the Rosen Morse potential are analyzed using hypergeometric method. Schrödinger equation of Rosen Morse potential is reduced into a second order differential equation of hypergeometric function by appropriate variable and parameters substitution. Energy spectrum is exactly obtained in the closed form and the wave functions are expressed in the form of hypergeometric polynomials /series. The graphs of the effective potential with the energy levels, groundstate, first and second excited  wave functions and its density probabilities are visualized using Delphi 7.0. Keywords: Hypergeometry, Rosen Morse potential, Energy spectrum, Wave function.