With a view to obtaining an exact closed form solution to the Schroedinger equation for a variety of hypercentral potentials, we investigate further application of an ansatz. This method is good enough for many kinds ...With a view to obtaining an exact closed form solution to the Schroedinger equation for a variety of hypercentral potentials, we investigate further application of an ansatz. This method is good enough for many kinds of potentials, but in this article it applies to a type of the hypercentral singular potentials V（x） = ax^2 ＋ bx^-4＋ cx^-6 and exponential hypercentral Morse potential U （x） = Uo （ e^-2ax - 2 e^-ax） for three interacting particles. The Morse potential is used for diatomic molecule while this method will be successfully used for many atomic molecules. The three-body potentials are more easily introduced and treated within the hyperspherical harmonic formalism. The internal particle motion is usually described by means of Jacobi relative coordinates p, A, and R, in terms of three particle positions r1, r2, and r3. We discuss some results obtained by using harmonic and anharmonic oscillators, however the hypercentral potential can be easily generalized in order to allow a systematic anaiysis, which admits an exact solution of the wave equation. This method is also applied to some other types of three-body, four-body, ..., interacting potentials.展开更多
文摘With a view to obtaining an exact closed form solution to the Schroedinger equation for a variety of hypercentral potentials, we investigate further application of an ansatz. This method is good enough for many kinds of potentials, but in this article it applies to a type of the hypercentral singular potentials V（x） = ax^2 ＋ bx^-4＋ cx^-6 and exponential hypercentral Morse potential U （x） = Uo （ e^-2ax - 2 e^-ax） for three interacting particles. The Morse potential is used for diatomic molecule while this method will be successfully used for many atomic molecules. The three-body potentials are more easily introduced and treated within the hyperspherical harmonic formalism. The internal particle motion is usually described by means of Jacobi relative coordinates p, A, and R, in terms of three particle positions r1, r2, and r3. We discuss some results obtained by using harmonic and anharmonic oscillators, however the hypercentral potential can be easily generalized in order to allow a systematic anaiysis, which admits an exact solution of the wave equation. This method is also applied to some other types of three-body, four-body, ..., interacting potentials.
