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18-4 |
Calculation using E = hn = hc/l. One of the points of this exercise is to look at the sizes of the energy values. An individual photon has a very small amount of energy but a mole of photons has a very significant amount of energy. |
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18-7 |
Calculate and compare the de Broglie wave lengths for a subatomic particle and for a macroscopic object. Remember that the distances between atoms that are covalently bonded are measured in Angstroms, which are 10-10 m or 10-8 cm. |
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18-10 |
A small exercise in counting variables. |
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18-11 |
A T/F questions about wavefunctions, especially complex wavefunctions. Levine’s T/F questions can be quite difficult but they are very instructive. When the answers to the problems are posted on this website the reasoning will be given. |
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18-17 |
A short T/F exercise about time-dependent vs. time-independent wavefunctions. |
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18-22 |
Calculation of the wavefunction for the transition of an electron confined to a short "box". Again, look at the sizes of the values. |
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18-23 |
Calculate the probability of finding a particle in the first quarter of its one-dimensionsional "box". Problem requires integration. It will probably be necessary to consult a simple table of integrals. Note that as n gets large the probability converges to its classical (or macroscopic) value. This convergence is required by the Correspondence Principle. |
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18-25 |
What do y and y2 look like for the n=4 and n=5 states of a particle in a one-dimensional "box"? |
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18-27 |
Calculate the smallest DE for a particle in a 1D "box" and then convert to the associated frequency (n = DE/h). |
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18-28 |
A different version of the previous problem. In some ways this problem is harder, but it is also easier because it is not necessary to use any fundamental constants. |
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18-31 |
An exercise is sketching wave functions and finding extrema. |
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18-32 |
A problem in working out energies and thinking about degeneracies for a particle in a 3D box. A straightforward extension of the 2D problem. |
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18-36 |
An exercise in working with operators. The point of part (a) is that the two operators do not commute, so the order in which they are applied matters. |
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18-40 |
An exercise that involves determining whether a function is an eigenfunction of a specific operator and, if so, determining its eigenvalue. |
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18-41 |
A problem in finding average values of some quantities for a particle in a 1D box. Two of the three parts were done in class. Use of an integral table is highly recommended. |
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18-45 |
A short problem about the harmonic oscillator. No calculation is necessary. |
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18-47 |
Find the most probable values, which are values for which the probability is a maximum, by taking the first derivative and setting it equal to zero. Note that the most probable value of the position is not necessarily equal to the average value of the position. |
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18-48 |
Demonstrate that y0 for the harmonic oscillator is a solution of the Schroedinger equation. This problem is a little messy, but several terms cancel in the end. |
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18-50 |
Calculation of average values for position, position squared, and momentum for the lowest energy state (or, the ground state) of the harmonic oscillator. Two of the integrals can be evaluated by looking at their symmetry. |
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18-52 |
An exercise related to the Correspondence Principle. The quantum numbers for macroscopic objects are so large that quantum effects are unimportant. |
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18-55 |
An exercise in application of the equations for the rigid rotor. |