Mapping Schr\"odinger equation into a Heun-type and identifying the corresponding potential function, energy and wavefunction
Abstract
We transform the Schr\"odinger wave equation to a nine-parameter Heun-type differential equation. Using our solutions of the latter in [J. Math. Phys. 59 (2018) 113507], we are able to identify the associated potential function, energy parameter, and write the corresponding wave function. Some of the solutions obtained correspond to new integrable quantum systems.
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