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Electron and deBroglie wavelength

  1. Jun 23, 2008 #1
    1. The problem statement, all variables and given/known data

    An electron moves in the x direction with the de Broglie wavelength 10^-8 cm.

    a) What is the energy of the electron in (eV)?
    b) What is the time-independent wavefunction of the electron?

    Solution?

    a) We have p = h/2pi * k = h/2pi * 2pi / lambda. So, p = h / lambda. Now, we need energy, so we have E = p^2 / 2m = h^2 / lambda ^2 * 1 / 2m = 2.40987e-17 J >> 150.142 eV.

    b) By Schroedinger's equation, we have

    [tex]-\frac{\hbar^2}{2m} \frac{\partial^2 \phi}{\partial x^2} = E \phi[/tex],

    so we have that

    [tex]\phi = Ae^{ikx} + Be^{-ikx} = Ae^{i \cdot 3.94784 \cdot 10^{21} \cdot x} + Be^{-i \cdot 3.94784 \cdot 10^{21} \cdot x}[/tex]
     
  2. jcsd
  3. Jun 23, 2008 #2

    kreil

    User Avatar
    Gold Member

    Do you have a question, or simply want the work checked....?
     
  4. Jun 23, 2008 #3
    The work checked was what I was looking for =)
     
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