# Quantum three-body problems

@article{Ma1999QuantumTP, title={Quantum three-body problems}, author={Zhong-Qi Ma}, journal={Science in China Series A: Mathematics}, year={1999}, volume={43}, pages={1093-1107} }

A scheme for dealing with the quantum three-body problem is presented to separate the rotational degrees of freedom completely from the internal ones. In this method, the three-body Schrodinger equation is reduced to a system of coupled partial differential equations, depending only upon three internal variables. For arbitrary total orbital angular momentum / and the parity (− 1)l+λ (λ = 0 or 1), the number of the equations in this system isl = 1 −λ. By expanding the wavefunction with respect…

## 8 Citations

### Quantum three-body system in D dimensions

- Physics, Mathematics
- 2002

The independent eigenstates of the total orbital angular momentum operators for a three-body system in an arbitrary D-dimensional space are presented by the method of group theory. The Schrodinger…

### Exact Solution to the Schrödinger Equation for the Quantum Rigid Body

- Physics
- 1999

The exact solution to the Schrödinger equation for the rigid body with the given angular momentum and parity is obtained. Since the quantum rigid body can be thought of as the simplest quantum…

### Analytical Structure Matching and Very Precise Approach to the Coulombic Quantum Three-Body Problem

- Physics
- 2001

A powerful approach to solve the Coulombic quantum three-body problem is proposed. The approach is exponentially convergent and more efficient than the hyperspherical coordinate method and the…

### EXACT SOLUTIONS TO THE N-BODY SCHRÖDINGER EQUATION FOR THE HARMONIC OSCILLATOR

- Physics
- 2000

The exact solutions to the N-body Schrödinger equation for the harmonic oscillator are presented analytically. The permutational symmetry of the solutions for the identical three-body system of the…

### Evaluation of Coulomb and exchange integrals for higher excited states of helium atom by using spherical harmonics series

- PhysicsJournal of Mathematical Chemistry
- 2012

In this work we study the higher excited states of Helium Atom. The purpose is to evaluate Coulomb and exchange integral via spherical harmonics series. The Coulomb and exchange integrals energy…

### Quantum states of hydrogen cations confined into spherical and nanotube-like potential wells: H2+ , H3+ (C 2h and C 2v ) and H3+ (D 3h )

- Chemistry, PhysicsPhysica Scripta
- 2021

In this work, the potential energy surfaces (PESs) of hydrogen-based cations H2+ and H3+ placed inside infinite potential wells, in the shape of an infinite cylinder and a sphere, are investigated.…

### Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras

- MathematicsFrontiers of Mathematics in China
- 2019

We give a classification of Lie bialgebra structures on generalized loop Schrödinger-Virasoro algebras $$\mathfrak{sv}$$sv. Then we find out that not all Lie bialgebra structures on generalized loop…

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