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By H. Dekker

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Extra resources for Classical and Quantum Mechanics of the Damped Harmonic Oscillator Dekker

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General Problems 49 •• Do Problem 48 for a particle in the first excited state (n ϭ 2). 61 • Can the expectation value of x ever equal a value that has zero probability of being measured? 50 •• Do Problem 48 for a particle in the second excited state (n ϭ 3). 51 •• The classical probability distribution function for a particle in a box of length L is given by P(x) ϭ 1/L. Use this to find ͳxʹ and ͳx 2ʹ for a classical particle in such a box. 52 •• (a) Find ͳxʹ for the first excited state (n ϭ 2) for a particle in a box of length L, and (b) find ͳx 2ʹ.

60 •• Calculate ͳxʹ and ͳx 2ʹ for the first excited state of the box described in Problem 59. 002L at (a) x ϭ L/2, (b) x ϭ 2L/3, and (c) x ϭ L. ) General Problems 49 •• Do Problem 48 for a particle in the first excited state (n ϭ 2). 61 • Can the expectation value of x ever equal a value that has zero probability of being measured? 50 •• Do Problem 48 for a particle in the second excited state (n ϭ 3). 51 •• The classical probability distribution function for a particle in a box of length L is given by P(x) ϭ 1/L.

5 eV. Find the work function ␾ of the cathode material. 78 •• A photon of energy E is scattered at an angle of ␪. Show that the energy EЈ of the scattered photon is given by EЈ ϭ E (E͞mec2)(1 Ϫ cos ␪) ϩ 1 79 •• A particle is confined to a one-dimensional box. 6 nm is emitted. 2 eV. Determine n. 4 eV. 7 nm it makes a transition to an excited state. 9 nm. What is the quantum number of the state to which the particle has decayed? 2 eV. 7 eV. Determine the work function of the surface and the wavelength ␭.

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