Pöschl–Teller potential

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

Moreover, eigenvalues and scattering data can be explicitly computed.

, 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]

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