Exact solution of Schroedinger equation in the case of reduction to Riccati type of ODE

Details Exact solution of Schroedinger equation in the case of reduction to Riccati type of ODE Exact solution of Schroedinger equation in the case of reduction to Riccati type of ODE

2011-01-16

arxiv.org/abs/1101.3075v1

Physics

General Physics

10 pages, 3 figures

Scientific paper

Here is presented a new type of exact solution of Schroedinger equation in the case of it's reduction to Riccati type of ordinary differential equations. Due to a very special character of Riccati's type equation, it's general solution is proved to have a proper gap of components of the particle wavefunction (which is known to be determining a proper quantum state of the particle). It means a possibility of sudden transformation or transmutation of quantum state of the particle (from one meaning of wavefunction to another), at definite moment of parametrical time. Besides, in the case of spherical symmetry of particle potential V in position space, as well as spherical symmetry of quantum system E total energy, such a solution is proved to be a multiplying of Bessel function (for radial component) & Legendre spherical function (for angle component), in spherical coordinate system.

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