p828aps5

# p828aps5 - Physics 828 Problem Set 5 Due Friday at...

This preview shows pages 1–2. Sign up to view the full content.

Physics 828: Problem Set 5 Due Friday, February 15, 2008 at beginning of class 1. Consider the one-dimensional harmonic oscillator with a quartic per- turbation. The Hamiltonian is then given by H = p 2 2 m + 1 2 kx 2 + λx 4 . (1) where k is the spring constant and λ is a parameter governing the size of the perturbing potential. (a) Calculate the perturbed energy levels to first order in λ . Hint: use the raising and lowering operators for the harmonic oscillator. (b). For a given λ , estimate the quantum number n where the first- order perturbation becomes inaccurate. (c). Write down formally the second order term to the energy correc- tion. Explain which matrix elements in the sum will be non-zero, and why. (d). What is the sign of the second-order correction for the ground state (n = 0)? 2. Consider a spin-1/2 particle in a time-independent external magnetic field B x ˆ x + B z ˆ z . Assume that the Hamiltonian is H = γ S · B , where γ > 0 and B x > 0.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern