You must read each slide, and complete any questions on the slide, in sequence.
One of the simplest problems in quantum physics is that of a particle inside a one-dimensional box. This Demonstration shows the time evolution of a packet constructed as a superposition of the first standing waves. The coefficients are such that in the limit the initial wave function would be a square pulse of half-width located at . With finite these two parameters control the position and width of the initial wave packet. You can follow the time evolution of the real and imaginary parts of the wave function, the probability distribution function, and the real part of the standing waves multiplied by their respective coefficients. The circles show the motion of the average position. Units: , and the width of the box is 1.
Use the Wolfram CDF Demonstration to answer the following questions:
1.
Calculate the quantum-mechanical zero-point energy of an electron confined within a one-dimensional box of length 1.0 nm.
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2.
The electrons within the π system of conjugated hydrocarbons may be treated as particles confined within a one-dimensional box. The lowest energy transition in the spectrum of buta-1,3-diene, C4H6, corresponds to excitation of an electron from the highest occupied energy level to the lowest unoccupied level and is observed in the ultraviolet region of the spectrum at a wavelength of 210 nm. Estimate the effective length of buta-1,3-diene.
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3.
An electron is confined to a circular ring of diameter 1.1 Å. Calculate the energy of the first excited rotational level.
