First order peturbation theory.

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SUMMARY

The discussion focuses on applying first-order perturbation theory to calculate the energy of the nth excited state of a spin-1/2 particle in an infinite symmetric potential well under a weak external magnetic field. The potential well is defined as V(x) = 0 for -L ≤ x ≤ L and V(x) = ∞ otherwise. The magnetic field is specified as B = -B k^ for -L ≤ x ≤ 0 and B = -B i^ for 0 ≤ x ≤ L. Participants emphasize the importance of defining the perturbed Hamiltonian and identifying the unperturbed eigenstates as critical steps in the calculation process.

PREREQUISITES
  • Understanding of quantum mechanics, specifically perturbation theory.
  • Familiarity with Hamiltonian operators and eigenstates.
  • Knowledge of the infinite potential well model.
  • Basic concepts of magnetic fields and their effects on quantum systems.
NEXT STEPS
  • Study the derivation of the perturbed Hamiltonian in quantum mechanics.
  • Learn about calculating energy corrections using first-order perturbation theory.
  • Explore the properties of eigenstates in infinite potential wells.
  • Investigate the effects of external magnetic fields on quantum particles.
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying quantum mechanics, as well as researchers and educators focusing on perturbation theory and its applications in quantum systems.

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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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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.
 

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