For a particle-in-a-box it can be shown that the possible energies are given by(adsbygoogle = window.adsbygoogle || []).push({});

[tex] E_n = \frac{n^2h^2}{8mL^2} [/tex]

where L is the length of the box. The corresponding momentum are given by:

[tex] p_n = \frac{nh}{2L} [/tex]

I don't think it's a problem that the energy has a definite value ([tex] \Delta E = 0 [/tex]) since it is a stationary state ([tex] \Delta t = \infty [/tex]).

But how is it possible for the momentum to be definite ([tex] \Delta p = 0 [/tex]) and, at the same time, the particle to be confined within the box ([tex] \Delta x < \infty [/tex]). Doesn't this violate the uncertainty principle [tex]

\Delta x \Delta p_x \geq \frac{h}{2\pi} [/tex].

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Particle-in-a-box and the uncertainty principle

**Physics Forums | Science Articles, Homework Help, Discussion**