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Solution of the Schrödinger Equation in Three Dimensions

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Abstract

In Section 9.5 the time-dependent Schrödinger equation for three-dimensional motion under the influence of a potential was separated with respect to time and space coordinates with the help of the ansatz
$$ \psi \left( {r,t} \right) = \exp \left[ { - \frac{i}{\hbar }Et} \right]{\varphi_E}(r) $$
. The three-dimensional stationary Schrödinger equation for the function φ E (r) obtained at the end of that section is
$$ \left[ { - \frac{{{\hbar^2}}}{{2M}}{\nabla^2} + V(r)} \right]{\varphi_E}(r) = E{\varphi_E}(r) $$
.

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Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  1. 1.Physics DepartmentSiegen UniversitySiegenGermany

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