# Time independent perturbation theory

• cks

#### cks

H=H0 + lambda * W

lambda << 1 must hold and the matrix elements of W are comparable in magnitude to those of H0.

More precisely, the matrix elements of W are of the same magnitude as the difference between the eigenvalues of H0.

I don't understand what is the meaning of " the matrix elements of W are of the same magnitude as the difference between the eigenvalues of H0".

(the above explanation are obtained from the SChaum's Outlines of Quantum Mechanics)

H=H0 + lambda * W

lambda << 1 must hold and the matrix elements of W are comparable in magnitude to those of H0.

More precisely, the matrix elements of W are of the same magnitude as the difference between the eigenvalues of H0.

I don't understand what is the meaning of " the matrix elements of W are of the same magnitude as the difference between the eigenvalues of H0".

it means that the matrix elements (the entries in the matrix) are about that same size as the difference between that eigenvalues of H0.

What exactly is it that you don't understand? Are you having trouble understanding what exactly those matrix elements are and why they are called matrix elements or is it something else?

the matrix elements of W are of the same magnitude as the difference between the eigenvalues of H0".

Let's say the matrix W=[2.2 3.1 4.1; 4.1 5.3 6.0; 7.3 8.2 9.3] (matlab code)

let's say the eigenvalues of H0 are 1 2 3 4 5 6 7 8 9

the matrix element 2.2 is roughly the same as the difference of the eigenvalues of 3-1. Am I understanding this correctly?

the matrix elements of W are of the "same magnitude"(don't understand what same magnitude means?) as the difference(difference? difference between which eigenvalues, in my example, there are 9 eigenvalues, which minus which is the difference the author is talking?) between the eigenvalues of H0".