Singular perturbation problem

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• Singular perturbation theory

  a1 + 2 a1 a2 = 0 ----> a2 = -1/2 a2^2 + 2 a1 a3 + a2 = 0 ----> a3 = +/- 1/[8 sqrt(3)] We explain singular perturbation theory and apply it to solve the problem.

• Perturbation Theory

  The programs are attached below as Q#.c where # corresponds to the question number I hope this helps Thanks again Yinon This solution helps with a perturbation theory problem.

• first-order energy correction in case of 1-D delta-function

  system and delta-function potential as perturbation.

• Perturbation Theory with Atoms

  Treat this as a perturbation on the Bohn Hamiltonian: Spin is irrelevant to this problem, so ignore it. a. Show that the ground state energy is not affected by this perturbation, in first order b.

• Perturbation of a negative potential time dependent problem

  This should set you in the right direction for the solution of this problem. This solution is provided in 737 words. It discusses how to solve the problem using perturbation theory and Euler's identiy.

• First order time dependent perturbation theory problem

  333999 Time dependent perturbation theory problem A system is in an eigenstate | psi_i > with energy E_i. The perturbation V(t) = H'exp(-((alpha)^2)(t^2)) is turned on at t_i = -infinity and left on until t_f = infinity.

• Perturbation theory applied to electron in a magnetic field

  But the eigenvalues are clearly given by: E = u_b |B| and E = -u_b |B|, with B = sqrt(B_z^2 + B_x^2) We can also solve this problem by diagonalizing the Hamiltonian.

• Shift in hydrogen ground state energy due to proton size

  In this problem, the unperturbed Hamilonian H_0 is: H_0 = p^2/(2m) - e^2/(4 pi epsilon_0 r) If we treat the proton as a uniformly charged sphere of radius R, the potential energy term in H_0 is not correct inside this sphere.

• Variational perturbation theory

  We then note that we indeed cannot put p = 1 and lambda = 0 as that leads to singular terms.