# Heun-Polynomial Representation of Regular-at-Infinity Solutions for the Basic SUSY Ladder of Hyperbolic P\"oschl-Teller Potentials Starting from the Reflectionless Symmetric Potential Well

@article{Natanson2014HeunPolynomialRO, title={Heun-Polynomial Representation of Regular-at-Infinity Solutions for the Basic SUSY Ladder of Hyperbolic P\"oschl-Teller Potentials Starting from the Reflectionless Symmetric Potential Well}, author={Gregory A. Natanson}, journal={arXiv: Mathematical Physics}, year={2014} }

It is shown that the regular-at-infinity solution of the 1D Schrodinger equation with the hyperbolic Poschl-Teller (h-PT) potential with integer parameters is expressible in terms of a n-order Heun polynomial in y=thr at an arbitrary negative energy. It was proven that the Heun polynomials in question form a subset of generally complex Lambe-Ward polynomials corresponding to zero value of the accessory parameter. Since the mentioned solution expressed in the new variable y has an almost… CONTINUE READING

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