Basic Principles of the Zero-Range Potential Method
It is known that the Schrödinger equation admits solutions expressible in a closed analytic form in only a few cases. The stationary Schrödinger equation is solvable analytically for a harmonic oscillator, for a particle moving in a Coulomb field or in a rectangular potential well, and in some other cases. Even the one-particle Schrödinger equation cannot be solved exactly for the great majority of potentials. In the case of the many-particle and non-stationary problems the situation becomes even more intractable.
KeywordsWave Function Atomic Physic Schrodinger Equation Separable Potential Coulomb Field
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