Symplectic Schemes and the Shooting Method for Eigenvalues of the Schrödinger Equation
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Abstract
The one-dimensional time-independent Schrödinger equation is transformed into a Hamiltonian canonical equation by means of the Legendre transformation, then the symplectic schemes and a new shooting method extended to the eigenvalues of the Schrödinger equation. The method is applied to the calculations of one-dimensional harmonic oscillator, an anharmonic oscillator and the hydrogen atom. The numerical results are in good agreement with the exact ones.
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