DOI: https://doi.org/10.30970/jps.04.141
POLYNOMIAL APPROACH AND POINT CANONICAL TRANSFORMATIONS IN THE CONSTRUCTING OF QUASI-EXACTLY SOLVABLE QUANTUM MECHANICAL POTENTIALS
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Journal of Physical Studies 4(2), 141–148 (2000)
DOI: https://doi.org/10.30970/jps.04.141 POLYNOMIAL APPROACH AND POINT CANONICAL TRANSFORMATIONS IN THE CONSTRUCTING OF QUASI-EXACTLY SOLVABLE QUANTUM MECHANICAL POTENTIALS |
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State University "Lvivska Politekhnika",
12 S. Bandery Str., Lviv, UA-79013, Ukraine
In this paper the polynomial approach for the constructing of quasi-exactly solvable potentials of Schrödinger equation is generalized. On this basis new potentials with $n$ wave functions and energy levels known are found. Two quasi-exactly solvable potentials with $N$ eigenstates found ($N$ is an integer number, depending on the parameters of potentials) were derived with the help of point canonic transformations. These potentials differ from the ones that were solved exactly by the feature in that their shape depends on the relation between the potentials parameters. Thus in the potential with two wells the barrier vanishes for some values of the parameters.
PACS number(s): 03.65.-w; 03.65.Ge