TY - JOUR
T1 - Exact solutions of the Schrödinger equation for some quantum-mechanical many-body systems
AU - Zhang, Ruiqin
AU - Deng, Conghao
PY - 1993
Y1 - 1993
N2 - We have solved exactly the Schrödinger equation in hyperspherical coordinates for some quantum-mechanical many-body systems. These systems, which interact with Coulomb, inverse-square, harmonic-oscillator, dipole, or Yukawa potentials, etc., can be solved in a similar way. Wave functions are expanded into orthonormal complete basis sets of the hyperspherical harmonics of hyperangles and generalized Laguerre polynomials of the hyperradius. The eigenvalues can be obtained explicitly by solving a simple secular equation. The results of practical calculations of Coulomb potential systems, such as H, He, and H-, etc., agree well with the reported exact ones. © 1993 The American Physical Society.
AB - We have solved exactly the Schrödinger equation in hyperspherical coordinates for some quantum-mechanical many-body systems. These systems, which interact with Coulomb, inverse-square, harmonic-oscillator, dipole, or Yukawa potentials, etc., can be solved in a similar way. Wave functions are expanded into orthonormal complete basis sets of the hyperspherical harmonics of hyperangles and generalized Laguerre polynomials of the hyperradius. The eigenvalues can be obtained explicitly by solving a simple secular equation. The results of practical calculations of Coulomb potential systems, such as H, He, and H-, etc., agree well with the reported exact ones. © 1993 The American Physical Society.
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U2 - 10.1103/PhysRevA.47.71
DO - 10.1103/PhysRevA.47.71
M3 - 21_Publication in refereed journal
VL - 47
SP - 71
EP - 77
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 2469-9926
IS - 1
ER -