Consider a particle of mass m that can exist only between

Chapter , Problem 60

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Consider a particle of mass m that can exist only between x 5 0 m and x 5 1L on the x axis. We could say that this particle is confi ned to a box of length L. In this situation, imagine the standing de Broglie waves that can fi t into the box. For example, the drawing shows the fi rst three possibilities. Note in this picture that there are either one, two, or three half-wavelengths that fi t into the distance L. Use Equation 29.8 for the de Broglie wavelength of a particle and derive an expression for the allowed energies (only kinetic energy) that the particle can have. This expression involves m, L, Plancks constant, and a quantum number n that can have only the values 1, 2, 3, . . . .