<正> With a view to obtaining an exact closed form solution to the Schr(o|¨)dinger.equation for a variety ofhypercentral potentials,we investigate further application of an ansatz.This method is good enough...<正> With a view to obtaining an exact closed form solution to the Schr(o|¨)dinger.equation for a variety ofhypercentral potentials,we investigate further application of an ansatz.This method is good enough for many kinds ofpotentials,but in this article it applies to a type of the hypercentral singular potentials V(x)=ax~2+bx~(-4)+cx~(-6) andexponential hypercentral Morse potential U(x)=Uo(e~(-2ax)-2e~(-ax))for three interacting particles.The Morse potentialis used for diatomic molecule while this method will be successfully used for many atomic molecules.The three-bodypotentials are more easily introduced and treated within the hyperspherical harmonic formalism.The internal particlemotion is usually described by means of Jacobi relative coordinates p,λ,and R,in terms of three particle positions γ_1,γ_2,and γ_3.We discuss some results obtained by using harmonic and anharmonic oscillators,however the hypercentralpotential can be easily generalized in order to allow a systematic analysis,which admits an exact solution of the waveequation.This method is also applied to some other types of three-body,four-body,...,interacting potentials.展开更多
文摘<正> With a view to obtaining an exact closed form solution to the Schr(o|¨)dinger.equation for a variety ofhypercentral potentials,we investigate further application of an ansatz.This method is good enough for many kinds ofpotentials,but in this article it applies to a type of the hypercentral singular potentials V(x)=ax~2+bx~(-4)+cx~(-6) andexponential hypercentral Morse potential U(x)=Uo(e~(-2ax)-2e~(-ax))for three interacting particles.The Morse potentialis used for diatomic molecule while this method will be successfully used for many atomic molecules.The three-bodypotentials are more easily introduced and treated within the hyperspherical harmonic formalism.The internal particlemotion is usually described by means of Jacobi relative coordinates p,λ,and R,in terms of three particle positions γ_1,γ_2,and γ_3.We discuss some results obtained by using harmonic and anharmonic oscillators,however the hypercentralpotential can be easily generalized in order to allow a systematic analysis,which admits an exact solution of the waveequation.This method is also applied to some other types of three-body,four-body,...,interacting potentials.
