Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Chapter 38, Problem 15Q
To determine

The probability density of a particle in infinite potential well for large values of n and whether the prediction approach accord with the correspondence principle.

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For a particle in a box, what would the probability distribution function Ic I2 look like if the particle behaved like a classical (Newtonian) particle? Do the actual probability distributions approach this classical form when n is very large? Explain.
For a classical system of non-interacting particles in the presence of a spherically symmetric potential V (r ) = yr, what is the mean energy per particle? y is a constant.
Problem 3. Consider the two example systems from quantum mechanics. First, for a particle in a box of length 1 we have the equation h² d²v EV, 2m dx² with boundary conditions (0) = 0 and V(1) = 0. Second, the Quantum Harmonic Oscillator (QHO) = h² d² +kr²V = EV 2m dg²+ka² 1/ k2²) v (a) Write down the states for both systems. What are their similarities and differences? (b) Write down the energy eigenvalues for both systems. What are their similarities and differences? (c) Plot the first three states of the QHO along with the potential for the system. (d) Explain why you can observe a particle outside of the "classically allowed region". Hint: you can use any state and compute an integral to determine a probability of a particle being in a given region.

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Physics for Scientists and Engineers with Modern Physics

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