Perturbation Theory by Blue Jay Lyrics
Alright so it's already three days later and by now you should've finished reading the First Look at Perturbation theory by James G Simmonds and and James E Mann Jr. And also brushed on until chapter 5 of Eigenvalue: General... And now we can begin the intro to pertubation theory which is quantum mechanics.
Perturbation theory is a set of approximation schemes for describing complicated quantum systems simply. Start with a simple system for which a mathematical solution is known, add an additional "perturbing" Hamiltonian representing a weak disturbance to the system and we go from there. If the disturbance is small enough, the physical quantities associated with the perturbed system (energy levels and eigenstates) can be expressed as "corrections" to those of the simple system. These corrections are small compared to the size of the quantities themselves, and can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. It describes a complicated unsolved system using a simple, solved system.
Upon adding a disturbance, also called a perturbative electric potential, which has to be small enough. Small shifts happen in the spectral lines of the hydrogen atom. (Stark Effect) We can calculate these shifts, not entirely exactly, but approximately enough to be accurate at the atomic level, also known as "good enough" by using approximations. The sum of the Columb Potential is unstable and often times hard to replicate and formulate.
The expressions are not exact, but they lead to accurate results as long as the expansion parameter is very small. Typically, the results are expressed in terms of finite power series in α that seem to converge to the exact values when summed to a higher order. However, after a certain order n ~ 1/α, the results become increasingly worse because of divergence. There are ways to convert them into convergent series, which can be evaluated for large-expansion parameters, most efficiently by the variational method. These corrections are what increase the precision of these measuring methods. The Hamiltonian has several corrections depending on the state of l, s, d, and the n as well. The relativistic H is only the basis which is then appended to Hpauli, and even further to HDarwin (not the biologist) that correction takes in consideration even the potential energy of the laplatian. By setting the particle superposition in between values of L in which L is 0. Which obviously requires you to normalize it properly.
So basically
Enoo= alpha^4mc^2(1/2n^3)
That's valid for states in which l is 0
In DeltaHspinorbit the proton creates an electric field as the electron moves the Electric field interacts with the dipole moment and the electron feels a spread momentum
So -eϕ(r)
In the next class you should have calculated all of possibilities of the Hamiltonians.
Perturbation theory is a set of approximation schemes for describing complicated quantum systems simply. Start with a simple system for which a mathematical solution is known, add an additional "perturbing" Hamiltonian representing a weak disturbance to the system and we go from there. If the disturbance is small enough, the physical quantities associated with the perturbed system (energy levels and eigenstates) can be expressed as "corrections" to those of the simple system. These corrections are small compared to the size of the quantities themselves, and can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. It describes a complicated unsolved system using a simple, solved system.
Upon adding a disturbance, also called a perturbative electric potential, which has to be small enough. Small shifts happen in the spectral lines of the hydrogen atom. (Stark Effect) We can calculate these shifts, not entirely exactly, but approximately enough to be accurate at the atomic level, also known as "good enough" by using approximations. The sum of the Columb Potential is unstable and often times hard to replicate and formulate.
The expressions are not exact, but they lead to accurate results as long as the expansion parameter is very small. Typically, the results are expressed in terms of finite power series in α that seem to converge to the exact values when summed to a higher order. However, after a certain order n ~ 1/α, the results become increasingly worse because of divergence. There are ways to convert them into convergent series, which can be evaluated for large-expansion parameters, most efficiently by the variational method. These corrections are what increase the precision of these measuring methods. The Hamiltonian has several corrections depending on the state of l, s, d, and the n as well. The relativistic H is only the basis which is then appended to Hpauli, and even further to HDarwin (not the biologist) that correction takes in consideration even the potential energy of the laplatian. By setting the particle superposition in between values of L in which L is 0. Which obviously requires you to normalize it properly.
So basically
Enoo= alpha^4mc^2(1/2n^3)
That's valid for states in which l is 0
In DeltaHspinorbit the proton creates an electric field as the electron moves the Electric field interacts with the dipole moment and the electron feels a spread momentum
So -eϕ(r)
In the next class you should have calculated all of possibilities of the Hamiltonians.