Supersymmetry in atomic physics and the radial problem
TL;DR: In this paper, a correct procedure for constructing supersymmetry in 3D is presented and the degeneracies are found between states of the same l but different n and Z and the previous results on the Coulomb and the three-dimensional isotropic oscillator problems are reestablished.
Abstract: A correct procedure for constructing supersymmetry in three dimensions is presented. The degeneracies are found between states of the same l but different n and Z and the previous results on the Coulomb and the three-dimensional isotropic oscillator problems are reestablished. The authors also consider the hydrogen-helium problem and find supersymmetry to hold to a good approximation.
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TL;DR: In this paper, a simple method of constructing potentials which is related to the work of Bhattacharjie and Sudarshan (1962) and for which the Schrodinger equation can be solved in terms of known special functions was investigated.
Abstract: The author investigates a simple method of constructing potentials which is related to the work of Bhattacharjie and Sudarshan (1962) and for which the Schrodinger equation can be solved in terms of known special functions. It turns out that this method can be related to supersymmetric quantum mechanics and this relationship can help to decide which special functions, satisfying linear homogeneous second-order differential equations, can be solutions of the Schrodinger equation with potentials of the form V(x)=W2(x)-W'(x). The author illustrates this procedure with the example of orthogonal polynomials and obtains explicit expressions of wavefunctions of a wide class of shape-invariant potentials.
258 citations
TL;DR: In this article, the Tietz potential for the scalar and vector interactions beside a Coulomb tensor term is used to investigate relativistic symmetries of the Dirac equation.
Abstract: Relativistic symmetries of the Dirac equation, namely the spin and pseudospin symmetries, are investigated under the Tietz potential for the scalar and vector interactions beside a Coulomb tensor term. The analytical approach of supersymmetry quantum mechanics is applied to the problem and the problem is discussed in a quite detailed manner.
81 citations
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TL;DR: In this paper, the Dirac canonical quantization method is implemented for the Lagrangian formalism with N = 2 supersymmetry in terms of two Grassmann variables in Classical Mechanics.
Abstract: Starting with the Lagrangian formalism with N=2 supersymmetry in terms of two Grassmann variables in Classical Mechanics, the Dirac canonical quantization method is implemented. The N=2 supersymmetry algebra is associated to one-component and two-component eigenfunctions considered in the Schr\"odinger picture of Nonrelativistic Quantum Mechanics. Applications are contemplated.
51 citations
TL;DR: In this paper, a method based on supersymmetric quantum mechanics is given for obtaining exact solutions of the potential V(r)=\ensuremath{\alpha}/r+${\mathit{p}}_{1}$r +${p{p]-2}$+${mathit{\p]-3}+$ {p]-4}
Abstract: A method based on supersymmetric quantum mechanics is given for obtaining exact solutions of the potential V(r)=\ensuremath{\alpha}/r+${\mathit{p}}_{1}$r+${\mathit{p}}_{2}$${\mathit{r}}^{2}$+${\mathit{p}}_{3}$${\mathit{r}}^{3}$+${\mathit{p}}_{4}$${\mathit{r}}^{4}$ where \ensuremath{\alpha} and the p's are parameters, provided certain relations are satisfied between the parameters. Detailed results are given for three specific cases. The potential in question gives rise to some very interesting shapes (double-well, etc.). The applicability of the shifted 1/N expansion method to such potential shapes is examined by comparing eigenenergies obtained by this method with the exact ones obtained from supersymmetric considerations. It is found that in certain situations, the shifted 1/N expansion method may give poor or erroneous results. Applicability of the proposed method to potentials involving higher powers of r is also discussed.
51 citations
TL;DR: In this article, the relativistic problem of spinless particles with position-dependent mass subject to kink-like potentials was investigated and the functional analysis method was used to obtain the bound state solutions in the closed form.
Abstract: The relativistic problem of spinless particles with position-dependent mass subject to kink-like potentials (~tanh αx) is investigated. By using the basic concepts of the supersymmetric quantum mechanics formalism and the functional analysis method, we solve exactly the position-dependent effective mass Klein–Gordon equation with the vector and scalar kink-like potential coupling, and obtain the bound state solutions in the closed form. It is found that in the presence of position-dependent mass there exists the symmetry that the discrete positive energy spectra and negative energy spectra are symmetric about zero energy for the case of a mixed vector and scalar kink-like potential coupling, and in the presence of constant mass this symmetry only appears for the cases of a pure scalar kink-like potential coupling or massless particles.
48 citations
Cites methods from "Supersymmetry in atomic physics and..."
...The supersymmetric approach has been extensively used to solving the Schrödinger equation [42–47], Klein–Gordon [48–50], Dirac equation [51–54] and DKP equation [55] in the presence of a constant mass....
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TL;DR: In this article, general conditions for dynamical supersymmetry breaking are discussed and examples are given (in 0 + 1 and 2 + 1 dimensions) in which such a program in four dimensions is possible.
3,270 citations
TL;DR: In this article, the properties of supersymmetric quantum mechanics for a class of models proposed by Witten were reviewed using both Hamiltonian and path integral formulations, and general conditions for which supersymmetry is broken (unbroken) by quantum fluctuations.
453 citations
TL;DR: In this article, a hierarchy of non-relativistic Hamiltonians with the property that the adjacent members of the hierarchy are supersymmetric partners is constructed, i.e. they share the same eigenvalue spectrum except for the missing ground state and the eigenvectors are simply related.
Abstract: The author presents a systematic procedure for constructing a hierarchy of non-relativistic Hamiltonians with the property that the adjacent members of the hierarchy are 'supersymmetric partners' i.e. they share the same eigenvalue spectrum except for the 'missing' ground state and the eigenvectors are simply related.
192 citations
TL;DR: In this article, it was shown that supersymmetric quantum mechanics may be used to interrelate the spectra of different atoms and ions, but supersymmetry is broken by electron-electron interactions.
Abstract: We show that supersymmetric quantum mechanics may be used to interrelate the spectra of different atoms and ions. This supersymmetry is broken by electron-electron interactions.
115 citations