Quantum Mechanics II PREFLIGHT

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The following three questions refer to the material you were to read in preparation for the lesson. Questions one and three require you to write a three or four sentence response. Number two is a multiple choice question. Click in the appropriate circle.

You may change your mind as often as you wish. When you are satisfied with your responses, click the SUBMIT button at the bottom of this page. Don't submit more than once. (If you absolutely HAVE to resubmit it, put a note on the end to that effect.)




1. Bohr Atom

URL: http://home.a-city.de/walter.fendt/physengl/bohrengl.htm
© Walter Fendt, May 30, 1999


In the above applet, two views of a hydrogen atom are given, the "wave" picture of deBroglie, and the "quantum" picture of Bohr. You might try right-clicking the mouse to drag an electron orbit in between quantum numbers. What happens to the wave picture? (That blue line is one wavelength.) What happens to the quantum picture?

Okay now that you've understood the two pictures, here's the problem. Einstein said that the frequency of light depended on E/h, so as the energy went higher, the wavelength got shorter. Bohr said that as the energy of the electron was greater, it orbited at higher quantum numbers, which DeBroglie interpreted as standing waves of constant wavelength. How is it that the Einstein picture changes the wavelength with energy, but the Bohr/deBroglie picture doesn't? Is there a contradiction here?




2.

A hydrogen atom is nicely explained with the Bohr model, but life gets complicated with more than one electron. Helium with 2 electrons can be solved (with great effort) but more complicated atoms are "approximated" with computer solutions. However, atoms that have lost all but one electron are said to be "hydrogen-like" with relatively simple spectra. From what you have read, would you expect a He+ ion to have a spectrum:

Like Hydrogen, but shifted blue.

Like Hydrogen, but shifted red.

Identical with Hydrogen.

Unlike Hydrogen (no Lyman series)

Why?


3. Particle in a Box

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This is a realization of one of the classic formal problems in quantum mechanics: the particle in a box. Imagine that a very small, light particle like an electron is trapped in the box formed by the thick black borders on the previous page. The principles of quantum mechanics tell us that the total energy of the particle in this box must change in fixed, discrete (quantum!) leaps. The RED horizontal lines drawn across the box show the energies a particle in this box can have. The height of each line above the box floor corresponds to the value of the energy: a higher line means a higher energy.

The primeval quantity in the simplest formulations of quantum mechanics is the wavefunction. This beast tells you everything you can know about the particle. In particular the square of the wavefunction tells you the probability of finding the particle as a function of position. The BLUE lines on the previous page show the wavefunctions that correspond to each allowed energy. Just so that the wavefunctions don't lie on top of one another, and to allow you to easily match a wavefunction with its corresponding energy, each wavefunction is drawn with its x-axis lying along the red line indicating its energy.

Now comes the fun part. You are not looking at a static picture. See the green section of the box floor? You can drag it up with your mouse, forming a little "pedestal" in the middle of the box. Just move your mouse arrow over the green section, press down the mouse button, and drag the mouse while holding down the mouse button. Release the button when you have the pedestal as tall as you'd like it. Once you have the pedestal up, you can also grab its sides and make it as wide or narrow as you like.

Okay, back to quizzes. How can you make the 1st and 2nd energy levels collapse into one? Why does this happen?





honors extra

This EPR paradox at the end of the chapter, called "Quantum Weirdness" is bothering me. Instead of Sally and Sam being in Los Angelos and Boston, lets put Sally on Alpha Centauri, 4 light-years away. They've got this plan, if ever Sally is in trouble, she will eat all her green jelly beans, and Sam will discover his pocket is full of red ones. Every once in a while, Sam eats a jelly bean, and if he gets 5 red ones in a row, he's supposed to send the Enterprise to pick up Sally. (Warp drive of course.) Now doesn't that mean that messages can travel faster than the speed of light? Does Quantum Mechanics violate Einstein's Relativity?





Below is a space for your thoughts, including general comments about today's assignment (what seemed impossible, what reading didn't make sense, what we should spend class time on, what was "cool", etc.):




You may change your mind as often as you wish. When you are satisfied with your responses, click the SUBMIT button.

I received no help from anyone on this assignment.