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Time-Independent Schrödinger Equation – Approximations
In Chapters 3, 6, 7 and 8, the Schrödinger equation was solved for a number of simple potentials. However, only in a very few cases, such exact analytical solutions for Schrödinger equations are available. For other potentials, we have to resort various kinds of approximations. For time-independent Schrödinger equations, broadly we consider three kinds of approximations: perturbation theory, variation method and WKB approximation.
A. Time-Independent Perturbation Theory
In perturbation theory, we split the Hamiltonian into two parts, H0 and λH′.
The Hamiltonian H0 is chosen in such a ...
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