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Darboux transformations and New exactly solvable potentials
C. Sivakumar, P. T. Varghese and K. Babu Joseph
Maharaja's College, Ernakulam, Kerala
A large number of exactly solvable quantum mechanical potential problems are formed using a technique called Darboux transformations(DT). The similarity between the eigen value spectra of the new and original Hamiltonian is shown. We generated exactly solvable potentials from harmonic oscillator potential and Coulomb potential and for the latter we developed a modified DT to get new potential problems.
Darboux theorem, Harmonic oscillator potential, Coulomb potential