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QUASICLASSICAL ANALYSIS OF THREE-DIMENSIONAL SCHRÖDINGER'S EQUATION AND ITS SOLUTION
2000
Modern Physics Letters A
The three-dimensional Schredinger's equation is analyzed with the help of the correspondence principle between classical and quantum-mechanical quantities. Separation is performed after reduction of the original equation to the form of the classical Hamilton-Jacobi equation. Each one-dimensional equation obtained after separation is solved by the conventional WKB method. Quasiclassical solution of the angular equation results in the integral of motion $\vec M^2=(l+\frac 12)^2\hbar^2$ and the
doi:10.1142/s0217732300000104
fatcat:ufzxerpygvephbr73jdgpiiqlm