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].

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

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