interaction potentials

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1: 15.18 Physical Applications

… ►The hypergeometric function has allowed the development of “solvable” models for one-dimensional quantum scattering through and over barriers (Eckart (1930), Bhattacharjie and Sudarshan (1962)), and generalized to include position-dependent effective masses (Dekar et al. (1999)). ►More varied applications include photon scattering from atoms (Gavrila (1967)), energy distributions of particles in plasmas (Mace and Hellberg (1995)), conformal field theory of critical phenomena (Burkhardt and Xue (1991)), quantum chromo-dynamics (Atkinson and Johnson (1988)), and general parametrization of the effective potentials of interaction between atoms in diatomic molecules (Herrick and O’Connor (1998)).

2: 18.39 Applications in the Physical Sciences

… ►The eigenvalues and radial wave functions are independent of $m_l$ and they both do depend on $l$ due to the presence of the ‘fictitious’ centrifugal potential ${\mathrm{\hslash }}^{2}l(l+1)/(2m{r}^2)$, which is a result of the choice of co-ordinate system, and not the physical potential energy of interaction $V(r)$. … ►For the potential $V(r)=+Z{e}^2/r$, corresponding to interaction of particles with like charges, there are no bound states, the continuum scattering states form a complete set for each $l$, as discussed in Chapter 33, and their discretized versions in §18.39(iv). …

3: DLMF Project News

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4: Bibliography D

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Wave function for smooth potential and mass step. Phys. Rev. A 59 (1), pp. 107–112.

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§15.18.

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Texas Instruments, Inc..

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Symbolic and extended-precision numerical computing system.

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§ ‣ Software Cross Index, § ‣ Software Cross Index.

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Supersymmetry, shape invariance, and exactly solvable potentials. Amer. J. Phys. 56, pp. 163–168.

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§18.38(iii).

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