Online Test Banks
Score higher
See Online Test Banks
Learning anything is easy
Browse Online Courses
Mobile Apps
Learning on the go
Explore Mobile Apps
Dummies Store
Shop for books and more
Start Shopping

Finding the Total Energy Equation for Three-Dimensional Free Particle Problems

At some point, your quantum physics instructor may want you to find the total energy equation for three-dimensional free particle problems. The total energy of the free particle is the sum of the energy in three dimensions:

E = Ex + Ey + Ez

With a free particle, the energy of the x component of the wave function is


And this equation works the same way for the y and z components, so here’s the total energy of the particle:


Note that kx2 + ky2 + kz2 is the square of the magnitude of k — that is,


Therefore, you can write the equation for the total energy as


Note that because E is a constant, no matter where the particle is pointed, all the eigenfunctions of


are infinitely degenerate as you vary kx, ky, and kz.

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus

Inside Sweepstakes

Win $500. Easy.