Calculation of the Energy Eigenvalue of a-Quantum System in the Framework of-Supersymmetry and Shape Invariance

Abstract

We present the energy eigenvalues of modified Pschl-Teller potential,the N-dimensionalhydrogen atom,and the N-dimensional harmonic oscillator.The calculations are carried out in the framework of supersymmetry and shape invariance.The present energy spectrum formulas are consistent with the exact solutions obtained with the usual factorization method.

The Study on Hydrous Pyrolysis Experiments of Coal-Measure Source Rocks in Ordos Basin

“…At present, the study of coal-formed oil on Ordos basin show that hydrocarbon generation of Jurassic coal is finite [7] . The comparative study for pyrolysis process of coal and mudstone from the same strata is less than the pyrolysis experiment carried out independently of coal or mudstone of coal-measure source rock [8] . Therefore, this paper using the hydrous pyrolysis experiments of a semi-closed system studies on coal and mudstone from taiyuan formation in northeastern margin of Ordos Basin.…”

Identity for the Exponential-Type Molecule Potentials and the Supersymmetry Shape Invariance

“…Eckart potential,I 2 1 Hulthen potential,I 3 1 generalized Morse potential, W and four-parameter molecule potential,I 5 ~81 etc. Some of these potentials are supersymrrletric shape-invariant potentials with a translation of parametersJ 9 1 For the shape-invariant potentials, their exact energy levels can be obtained algebraically by making use of the supersymmetry shapemvariance approach^1 0 " 12 ! and the supersymmetric WKB approximation.…”

A New Type of Shape-Invariant Potential

“…Since the concept of shape invariance has been introduced by Gendenshtein,' 1 ' the relationship between shape-invariance and solvable potentials has been investigated extensively.' [2][3][4][5][6][7][8][9] ! Gendenshtein pointed out that essentially all the known solvable potentials are shape-invariant, and the energy eigenvalues can be calculated algebraically.…”