For a simple harmonic oscillator potential, Vo(x) =-kx ² =¬mo*x', %3D the ground state energy eigenvalue is EO ho and the ground state eigenfunction is a²x² то - exp where a? = Now suppose that the potential has a small perturbation, 1 1 Vo(x) =kx² → V(x) = kx² + àx°. Use perturbation theory to find the (first order) corrected eigenvalue, in terms of w. [7] 1x 3 x5x... x (2n – 1) 2n+1B" You will need: x2" exp(-ßx²) dx

For a simple harmonic oscillator potential, Vo(x) =-kx ² =¬mo*x', %3D the ground state energy eigenvalue is EO ho and the ground state eigenfunction is a²x² то - exp where a? = Now suppose that the potential has a small perturbation, 1 1 Vo(x) =kx² → V(x) = kx² + àx°. Use perturbation theory to find the (first order) corrected eigenvalue, in terms of w. [7] 1x 3 x5x... x (2n – 1) 2n+1B" You will need: x2" exp(-ßx²) dx

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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