Electron and deBroglie wavelength

[Domnu]

Homework Statement

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

$$-\frac{\hbar^2}{2m} \frac{\partial^2 \phi}{\partial x^2} = E \phi$$,

so we have that

$$\phi = Ae^{ikx} + Be^{-ikx} = Ae^{i \cdot 3.94784 \cdot 10^{21} \cdot x} + Be^{-i \cdot 3.94784 \cdot 10^{21} \cdot x}$$

 

[kreil]

Do you have a question, or simply want the work checked...?

 

[Domnu]

The work checked was what I was looking for =)