%0 Journal Article %1 Ho2014115 %A Ho, C.-L. %A Lee, J.-C. %A Sasaki, R. %D 2014 %J Annals of Physics %K equation mechanics physics quantum scattering schrodinger solution theory unread %N 0 %P 115-131 %R http://dx.doi.org/10.1016/j.aop.2014.01.015 %T Scattering amplitudes for multi-indexed extensions of solvable potentials %U http://www.sciencedirect.com/science/article/pii/S0003491614000220 %V 343 %X New solvable one-dimensional quantum mechanical scattering problems are presented. They are obtained from known solvable potentials by multiple Darboux transformations in terms of virtual and pseudo virtual wavefunctions. The same method applied to confining potentials, e.g. Pöschl–Teller and the radial oscillator potentials, has generated the multi-indexed Jacobi and Laguerre polynomials. Simple multi-indexed formulas are derived for the transmission and reflection amplitudes of several solvable potentials.

@article{Ho2014115, abstract = {New solvable one-dimensional quantum mechanical scattering problems are presented. They are obtained from known solvable potentials by multiple Darboux transformations in terms of virtual and pseudo virtual wavefunctions. The same method applied to confining potentials, e.g. Pöschl–Teller and the radial oscillator potentials, has generated the multi-indexed Jacobi and Laguerre polynomials. Simple multi-indexed formulas are derived for the transmission and reflection amplitudes of several solvable potentials.}, added-at = {2014-03-13T00:34:46.000+0100}, author = {Ho, C.-L. and Lee, J.-C. and Sasaki, R.}, biburl = {https://www.bibsonomy.org/bibtex/282818ffddc146090e90d8f70b296c6d1/drmatusek}, doi = {http://dx.doi.org/10.1016/j.aop.2014.01.015}, interhash = {683e6c200d8c8b5528446019c85b7306}, intrahash = {82818ffddc146090e90d8f70b296c6d1}, issn = {0003-4916}, journal = {Annals of Physics }, keywords = {equation mechanics physics quantum scattering schrodinger solution theory unread}, month = apr, number = 0, pages = {115-131}, timestamp = {2014-03-13T00:34:46.000+0100}, title = {Scattering amplitudes for multi-indexed extensions of solvable potentials }, url = {http://www.sciencedirect.com/science/article/pii/S0003491614000220}, volume = 343, year = 2014 }