First order peturbation theory.

Then you can use the first order perturbation theory to calculate the energy correction. Finally, you can use this correction to calculate the energy of the nth excited state.In summary, the conversation discusses the calculation of the energy of an excited state of a particle with mass m and spin 1/2 moving in an infinite, symmetric potential well under the influence of a weak external magnetic field. The first order perturbation theory is used to calculate the energy correction and ultimately determine the energy of the nth excited state. The relevant equation and process for the calculation are also mentioned.
  • #1
wgdtelr
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Homework Statement


A particle of mass m and spin 1/2 is moving in an infinite, symmetric potential well
V (x) = { 0 -L<= x <= L.
= ∞ otherwise..

Under the effect of a weak external magnetic field.
B = -B k^ ; -L <= x <= 0
= -B i^ 0 <= x <= L.
where i^ and k^ are the unit vectors along the Ox and Oz directions. Calculate, in the first order of perturbation theory, the energy of the nth exited state of the partic



The Attempt at a Solution



give me some hints to start this problem.
 
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  • #2
The energy calculation is fairly straightforward, do you know what the relevant equation is? As for the process, you need to first define what the perturbed Hamiltonian is and the unperturbed eigenstates are.
 

FAQ: First order peturbation theory.

What is first order perturbation theory?

First order perturbation theory is a mathematical technique used in quantum mechanics to approximate the energy levels and wavefunctions of a quantum system that has been slightly perturbed or disturbed from its original state. It allows us to calculate the effects of a perturbation on the system without solving the full Schrodinger equation.

How is first order perturbation theory applied?

First order perturbation theory involves calculating the first-order correction to the energy and wavefunction of a quantum system. This is done by adding a perturbation term to the original Hamiltonian and then solving the resulting equations using mathematical methods such as perturbation theory or matrix diagonalization.

What are the assumptions of first order perturbation theory?

The main assumptions of first order perturbation theory are that the perturbation is small compared to the original Hamiltonian, the perturbation is time-independent, and the perturbation does not significantly alter the form of the wavefunction. Additionally, the system should have a discrete energy spectrum.

What types of systems can first order perturbation theory be applied to?

First order perturbation theory can be applied to any quantum system with a discrete energy spectrum, such as a particle in a potential well, a harmonic oscillator, or an atom. It is particularly useful for systems that are difficult to solve using other analytical methods, such as multi-electron atoms.

What are the advantages of using first order perturbation theory?

First order perturbation theory allows us to approximate the energy levels and wavefunctions of a quantum system with a perturbation, without having to solve the full Schrodinger equation. It is a powerful tool for understanding the effects of small perturbations on quantum systems and is widely used in many areas of physics, including atomic and molecular physics, condensed matter physics, and quantum chemistry.

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