The Jost Solutions: Technical Details

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Body Problem ◽  
Complete Information ◽  
Two Body Problem ◽  
Jost Function ◽  
Radial Schrödinger Equation ◽  
Jost Functions ◽  
Technical Details ◽  
Jost Solutions

This chapter discusses the technical details of the Jost solutions of the Schrödinger equation. The nonrelativistic quantum mechanical two-body problem can be described in terms of the Jost functions and Jost solutions of the Schrödinger equation. When defined for all complex values of the momentum, the Jost functions contain complete information about the underlying physical system. Compared to the S-function which may have redundant poles, the Jost function is a more fundamental quantity because it does not suffer from ambiguities caused by redundant zeros. The chapter first considers the time-independent radial Schrödinger equation before analyzing the regular solution for the Jost function, the poles of the S-matrix, and the wavepacket approach.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

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