It's good to know that the electron is moving on a circular orbit; a very simple problem. But at the moment we are just able to describe a circular motion around the origin of the coordinates. Therefore we want to generalize our formulas (2a.05/06).
Till now we had just two parameters, the period T of the orbital motion (remember how we defined _B ) and the radius R of the circle. Here we want to introduce three additional ones:

The first parameter is the phase angle ₀: We draw a line from the center of the circle to the initial position. This line is called the radius vector. The name of the angle between the radius vector and the x-axis is called phase angle. With its help we can vary the initial position of the circulation.
Until now the circulation began at the point P( R | 0 ) (₀ = 0, see Fig.2). We want to construct motions with arbitrary phase angles ₀ , say ₀ = 45°. Thus our second ansatz looks:
(2c.01)
In this case our electron is located at (see Fig.3)

We summarize: Our new ansatz isn't as special as our first one, but also not general enough. There exists a more general solution which we want to investigate with you.
Besides the already introduced parameters, the radius R, the phase angle ₀ and the period T, we introduce - as we have announced - a fourth and a fifth parameter: x_C and y_C , the coordinates of the center of the circle. For example, if we choose x_C = 7R and y_C = - 1.5R, the center of our circle is the point P( 7R | - 1.5R ). So our most general ansatz looks:
(2c.02)

It's clear that all new parameters don't have any effect at the correctness of the solution (proof it by yourself like we did it!).
Finally we know about - an how to describe - the motion of our electron in an homogeneous constant magnetic field. We hope we gave you an adequate introduction into the foundations of the physics of the laser-driven starship.

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Chapter Two