Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Particle in a box problem

  1. Jun 17, 2017 #1
    Consider the particle in a box problem. The number of energy eigenbasis is 'countable' infinity. But the number of position eigenbasis is 'uncountable' infinity. x can take any value from the interval [0,L] Whichever basis I choose, shouldn't the dimensionality of the vector space be the same?
     
  2. jcsd
  3. Jun 17, 2017 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    That is true, iff the „eigenstates” are element of the same topological vector space. But the space of the eigenvectors of X is larger than the space of the eigenvectors of H, or, equivalently, the two spectral equations for X and H do not have solutions in the same space.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Particle in a box problem
  1. Particle in a box (Replies: 3)

  2. Particle in a box? (Replies: 8)

  3. Particle in Box (Replies: 3)

  4. Particle in a box (Replies: 3)

Loading...