What are the different ways to reduce the Schrödinger equation?
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There are different ways to reduce the Schrödinger equation. One approach is through the Legendre transform, which expresses the dynamics of a classical system through first-order Hamiltonian equations . Another approach is through discretization, where a discrete equation is derived as an exact discretization of the continuous Schrödinger equation . Additionally, there are numerical approaches such as variational and perturbational methods to obtain approximate solutions to the Schrödinger equation . These methods involve approximations and calculations of eigenvectors and eigenvalues of the equation . In quantum chemistry, the perturbational and variational approaches are commonly used, along with the adiabatic separation of fast and slow motions in molecular systems . The use of pseudopotentials is also mentioned as a way to reduce the complexity of the molecular electronic Schrödinger equation .
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| The paper briefly outlines the possibility of reducing the complexity of the molecular electronic Schrödinger equation by using pseudopotentials. | |
| The paper does not provide information on different ways to reduce the Schrödinger equation. The paper discusses the solution of the Schrödinger equation with periodic potentials and the truncation of an infinite matrix to a finite matrix. | |
| The paper does not provide information about different ways to reduce the Schrödinger equation. The paper discusses two numerical approaches, variational and perturbational, to obtain approximate solutions to the Schrödinger equation. | |
| The paper does not provide information about different ways to reduce the Schrödinger equation. | |
| The paper does not discuss different ways to reduce the Schrödinger equation. |
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