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# 1. Standing waves, momentum, and energy Now that you know how to relate wavelength and momentum, you can answer

many kinds of quantum mechanics questions. For the discussions in this problem, suppose you put up walls so that a particle can only move left and right between a wall at x = 0 and a wall at x = L. (This is also know as a “particle in a one-dimensional box”, the size of the “box” being L). a. Because the particle can only move left or right its motion is described by waves moving left and right. You already know that the superposition of a wave moving left and a wave moving right gives rise to standing waves and you know how to ﬁnd the wavelengths of these standing waves. Using the de Broglie relation between the momentum of the particle and its wavelength, p = h/λ, ﬁnd the two lowest possible momenta for this particle for each of the following three different values of L: i. L = size of your bedroom ii. L = rough size of an atom iii. L = rough size of a nucleus (Note: The standing wave patterns all have to be node-node patterns... Why?)

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