A class of exactly solvable potentials. I. One-dimensional Schrödinger equation

1983 ◽  
Vol 151 (1) ◽  
pp. 263
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
One Dimensional ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable

scholarly journals Hidden symmetry of the 16D oscillator and its 9D coulomb analogue

2020 ◽  
Vol 56 (2) ◽  
pp. 206-216
Author(s):  
А. N. Lavrenov ◽  
I. А. Lavrenov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Separation Method ◽  
Cylindrical Coordinates ◽  
Hidden Symmetry ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable

We present the quadratic Hahn algebra QH(3) as an algebra of the hidden symmetry for a certain class of exactly solvable potentials, generalizing the 16D oscillator and its 9D coulomb analogue to the generalized version of the Hurwitz transformation based on SU (1,1)⊕ SU (1,1)  . The solvability of the Schrodinger equation of these problems by the variables separation method are discussed in spherical and parabolic (cylindrical) coordinates. The overlap coefficients between wave functions in these coordinates are shown to coincide with the Clebsch – Gordan coefficients for the SU(1,1) algebra.

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