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The Hulthen potential is a short-range potential that behaves like a Coulomb potential for small values of but decreases exponentially for large values of . It has been applied to problems in nuclear, atomic and solid-state physics.

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Contributed by: S. M. Blinder (July 2020)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

To solve the Schrödinger equation, make the variable transformation with and define the constants

,

.

The differential equation becomes

,

subject to the boundary conditions and . The solution is found to be

.

The second boundary condition requires that

,

This leads to the forms of and given above.

References

[1] M. R. Setare and E. Karimi, "Algebraic Approach to the Hulthen Potential," *International Journal of Theoretical Physics*, 46(5), 2007 pp. 1381–1388. doi:10.1007/s10773-006-9276-z.

[2] J. Stanek, "The One-Dimensional Hulthén Potential in the Quantum Phase Space Representation," *Central European Journal of Physics*, 12(2), 2014 pp. 90–96. doi:10.2478/s11534-014-0433-3.

[3] S. Flügge, *Practical Quantum Mechanics*, New York: Springer, 1999 pp. 175–178.

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