Write the Schrodinger equation for zero order approximation of perturbation theory.
Question
Write the Schrodinger equation for zero order approximation of perturbation theory.
Solution
The Schrödinger equation for the zeroth order approximation in perturbation theory is simply the time-independent Schrödinger equation for the unperturbed system. This can be written as:
H^0 |ψ^0> = E^0 |ψ^0>
Here, H^0 is the Hamiltonian of the unperturbed system, |ψ^0> is the wave function of the system in the zeroth order approximation, and E^0 is the energy of the system in the zeroth order approximation.
The zeroth order approximation assumes that the perturbation is small enough that it does not significantly affect the system. Therefore, the solution to the Schrödinger equation for the zeroth order approximation is the same as the solution to the Schrödinger equation for the unperturbed system.
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Schrodinger wave equation
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