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Strange orbit in 3P21

As discussed in class, there is an ambiguity as to the direction in which the mass heads at the point 90° away from its initial position in problem 3P21. The movie shows what really happens.

How was the movie made? Start with the equation F = ma written in polar coordinates. Conservation of angular momentum about the origin constrains the tangential velocity. You can then (numerically) integrate the radial equation to get the trajectory. I did this integral in Mathematica. For more details, click here.

These movies illustrate some aspects of wave packet dynamics. They are stored in QuickTime format.

A Gaussian wave packet - This movie shows how a Gaussian wave packet with a nonzero expectation value of momentum evolves in time. Notice the difference between phase velocity and group velocity. Which is greater?
Moving beats - This shows the interference between two waves at slightly different frequencies. Are the phase velocity and group velocity of the two waves the same or different?
More moving beats - Two sine waves of nearly equal frequency beat with one another. If the waves travel with the same phase velocity, then the slowly varying envelope travelling at the group velocity moves at that same speed. This is true for light in vacuum. If one of the waves moves with a higher phase velocity than the other, then the group velocity differs from the phase velocity of either component wave. Which is the case for this movie?
A particle in a quadratic potential - This one shows how a wave packet in a simple harmonic oscillator potential well evolves in time. It's best viewed in a player that allows you to loop back and forth.

Moving beats

Moving beats - Two sine waves of nearly equal frequency beat with one another. If the waves travel with the same phase velocity, then the slowly varying envelope travelling at the group velocity moves at that same speed. This is true for light in vacuum. If one of the waves moves with a higher phase velocity than the other, then the group velocity differs from the phase velocity of either component wave. Which is the case for this movie?

A particle in a quadratic potential - This one shows how a wave packet in a simple harmonic oscillator potential well evolves in time. It's best viewed in a player that allows you to loop back and forth.

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Physics 24 at Harvey Mudd College
Updated 4/27/00

A Gaussian wave packet - This movie shows how a Gaussian wave packet with a nonzero expectation value of momentum evolves in time. Notice the difference between phase velocity and group velocity. Which is greater?
Moving beats - This shows the interference between two waves at slightly different frequencies. Are the phase velocity and group velocity of the two waves the same or different?
More moving beats - Two sine waves of nearly equal frequency beat with one another. If the waves travel with the same phase velocity, then the slowly varying envelope travelling at the group velocity moves at that same speed. This is true for light in vacuum. If one of the waves moves with a higher phase velocity than the other, then the group velocity differs from the phase velocity of either component wave. Which is the case for this movie?
A particle in a quadratic potential - This one shows how a wave packet in a simple harmonic oscillator potential well evolves in time. It's best viewed in a player that allows you to loop back and forth.