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

Homework Help: Particle in one-dimensional box

  1. Nov 12, 2008 #1
    By separation of variables, I have found that

    [tex]\frac{-\hbar}{2mg(x)}\frac{d^{2}g(x)}{dx^{2}} = \frac{i}{h(t)}\frac{d h(t)}{dt}[/tex]

    Both sides there have to equal the same constant. But why is this constant the total energy of the particle?
  2. jcsd
  3. Nov 12, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    The idea is that you have that Hamiltonian [tex]H = \frac{p^2}{2m} = -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial^2x}[/tex]. The energy of the particle are eigenvalues of the Hamiltonian, so [tex]H\psi=E\psi[/tex], so [tex]\frac{-\hbar^2}{2m}\frac{\partial^2}{\partial^2x}\psi=E\psi[/tex].

    (And in the way you wrote it, the constant won't be the energy of the particle, but rather the energy divided by hbar)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook