In mathematical physics, a Pöschl–Teller potential, named after the physicists Herta Pöschl [1] (credited as G. Pöschl) and Edward Teller, is a special class of potentials for which the one-dimensional Schrödinger equation can be solved in terms of special functions.
In its symmetric form is explicitly given by [2]
and the solutions of the time-independent Schrödinger equation
with this potential can be found by virtue of the substitution , which yields
Thus the solutions are just the Legendre functions with , and , . Moreover, eigenvalues and scattering data can be explicitly computed. [3] In the special case of integer , the potential is reflectionless and such potentials also arise as the N-soliton solutions of the Korteweg–De Vries equation. [4]
The more general form of the potential is given by [2]
A related potential is given by introducing an additional term: [5]
In mathematical physics, a Pöschl–Teller potential, named after the physicists Herta Pöschl [1] (credited as G. Pöschl) and Edward Teller, is a special class of potentials for which the one-dimensional Schrödinger equation can be solved in terms of special functions.
In its symmetric form is explicitly given by [2]
and the solutions of the time-independent Schrödinger equation
with this potential can be found by virtue of the substitution , which yields
Thus the solutions are just the Legendre functions with , and , . Moreover, eigenvalues and scattering data can be explicitly computed. [3] In the special case of integer , the potential is reflectionless and such potentials also arise as the N-soliton solutions of the Korteweg–De Vries equation. [4]
The more general form of the potential is given by [2]
A related potential is given by introducing an additional term: [5]