Parasupersymmetric Quantum Mechanics

• Main Authors: Yang-Rang Huang, 黃暘穰
• Other Authors: Wang-Chang Su
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/43191174194369691128

碩士 === 國立中正大學 === 物理所 === 97 === The purpose of this paper is constructing the formula of parasupersymmetric quantum mechanics (PSQM) and discussing its physical meaning. At first, we briefly review the supersymmetric quantum mechanics (SQM), as a preparation for PSQM. In the next chapter, we re-write the Hamiltonians of some simple one dimentional problems of quantum mechanics in algebratic form. Hence we find out that the superpotential of bound state differs from the superpotential of scattering state and that the QM systems in fermionic operator or bosonic operator form are different. In chapter three, we construct the PSQM formula. After reviewing previous results, we find out a relation from parafermionic operator of order three; From this, we obtain the general formula of arbitrary order p with given q. Therefore, when the parafermionic operator is replaced by supercharge, the formula is transformed into the combination of parasupersymmetric Hamiltonian H and supercharge. At the end, we find, under some conditions, the energy eigenvalues of H are necessarily nonnegative and all the excited state are (p + 1)-fold degenerate.