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ice109
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why in time independent degenerate perturbation we diagonalize the matrix of the perturbation part of the hamilitonian and not the original hamiltonian?
what? the bold part is true and i agree with.jensa said:Because the unperturbed part is just proportional to the unit matrix since all states in the degenerate subspace have the same energy.
Degenerate time-independent perturbation theory is a mathematical method used in quantum mechanics to calculate the energy levels and wavefunctions of a system when it is subject to a weak perturbation. It is specifically used for systems where multiple states have the same energy, known as degenerate states.
Degenerate time-independent perturbation theory is used when a system has degenerate states and the perturbation is weak enough that it does not significantly change the energy levels or wavefunctions of the system.
Degenerate time-independent perturbation theory works by first calculating the unperturbed energy levels and wavefunctions of the system. Then, the perturbation is introduced and the first-order correction to the energy levels and wavefunctions is calculated. This correction is added to the unperturbed values to obtain the perturbed values.
One limitation of degenerate time-independent perturbation theory is that it only works for weak perturbations. If the perturbation is strong, higher order corrections may need to be considered. Additionally, this method can only be applied to systems with degenerate states, so it is not applicable to all quantum mechanical systems.
Degenerate time-independent perturbation theory has many applications in physics, chemistry, and engineering. It is used in the study of atomic and molecular spectra, in the design of electronic devices, and in the analysis of quantum systems in condensed matter physics. It is also used in the development of quantum algorithms for computing and data encryption.